Adapter to combine observer and checker. Observer Checker voidconst State &Time observer_type &checker_type & ControlledStepperCheckercontrolled_stepper_tagAdapter to combine controlled stepper and checker. ControlledStepper Checker stepper_type::state_type stepper_type::value_type stepper_type::deriv_type stepper_type::time_type controlled_step_resultSystemStateInOut &time_type &time_type &forward of the do_step method stepper_type &checker_type &Construct the checked_stepper. DenseOutStepperCheckerdense_output_stepper_tagAdapter to combine dense out stepper and checker. DenseOutStepper Checker stepper_type::state_type stepper_type::value_type stepper_type::deriv_type stepper_type::time_type std::pair< time_type, time_type >System voidconst StateType &time_typetime_type voidtime_typeStateOut & voidtime_typeconst StateOut & const state_type &void time_typevoid const state_type &void time_typevoid time_typevoid stepper_type &checker_type &Construct the checked_stepper. StepperCheckerstepper_tagAdapter to combine basic stepper and checker. Stepper Checker stepper_type::state_type stepper_type::value_type stepper_type::deriv_type stepper_type::time_type voidSystemStateInOut &const time_typeconst time_typeforward of the do_step method stepper_type &checker_type &Construct the checked_stepper.

boost::enable_if< typename has_value_type< State >::type, size_t >::typeSystemThe system function to solve, hence the r.h.s. of the ordinary differential equation. State &The initial state. TimeStart time of the integration. TimeEnd time of the integration. TimeInitial step size, will be adjusted during the integration. ObserverObserver that will be called after each time step. Integrates the ODE. Integrates the ODE given by system from start_time to end_time starting with start_state as initial condition and dt as initial time step. This function uses a dense output dopri5 stepper and performs an adaptive integration with step size control, thus dt changes during the integration. This method uses standard error bounds of 1E-6. After each step, the observer is called.A second version of this function template exists which explicitly expects the value type as template parameter, i.e. integrate< double >( sys , x , t0 , t1 , dt , obs ); The number of steps performed. size_tSystemState &TimeTimeTimeObserver size_tSystemThe system function to solve, hence the r.h.s. of the ordinary differential equation. State &The initial state. TimeStart time of the integration. TimeEnd time of the integration. TimeInitial step size, will be adjusted during the integration. Integrates the ODE without observer calls. Integrates the ODE given by system from start_time to end_time starting with start_state as initial condition and dt as initial time step. This function uses a dense output dopri5 stepper and performs an adaptive integration with step size control, thus dt changes during the integration. This method uses standard error bounds of 1E-6. No observer is called.A second version of this function template exists which explicitly expects the value type as template parameter, i.e. integrate< double >( sys , x , t0 , t1 , dt ); The number of steps performed. size_tSystemState &TimeTimeTime

size_tStepperThe stepper to be used for numerical integration. SystemFunction/Functor defining the rhs of the ODE. State &The initial condition x0. TimeThe initial time t0. TimeThe final integration time tend. TimeThe time step between observer calls, not necessarily the time step of the integration. ObserverFunction/Functor called at equidistant time intervals. Integrates the ODE with adaptive step size. This function integrates the ODE given by system with the given stepper. The observer is called after each step. If the stepper has no error control, the step size remains constant and the observer is called at equidistant time points t0+n*dt. If the stepper is a ControlledStepper, the step size is adjusted and the observer is called in non-equidistant intervals. The number of steps performed. size_tStepperSystemconst State &TimeTimeTimeObserverSecond version to solve the forwarding problem, can be called with Boost.Range as start_state. size_tStepperSystemState &TimeTimeTimeintegrate_adaptive without an observer. size_tStepperSystemconst State &TimeTimeTimeSecond version to solve the forwarding problem, can be called with Boost.Range as start_state.

size_tStepperThe stepper to be used for numerical integration. SystemFunction/Functor defining the rhs of the ODE. State &The initial condition x0. TimeThe initial time t0. TimeThe final integration time tend. TimeThe time step between observer calls, not necessarily the time step of the integration. Observer[optional] Function/Functor called at equidistant time intervals. StepOverflowChecker[optional] Functor to check for step count overflows, if no checker is provided, no exception is thrown. Integrates the ODE with constant step size. Integrates the ODE defined by system using the given stepper. This method ensures that the observer is called at constant intervals dt. If the Stepper is a normal stepper without step size control, dt is also used for the numerical scheme. If a ControlledStepper is provided, the algorithm might reduce the step size to meet the error bounds, but it is ensured that the observer is always called at equidistant time points t0 + n*dt. If a DenseOutputStepper is used, the step size also may vary and the dense output is used to call the observer at equidistant time points. If a max_step_checker is provided as StepOverflowChecker, a no_progress_error is thrown if too many steps (default: 500) are performed without progress, i.e. in between observer calls. If no checker is provided, no such overflow check is performed. The number of steps performed. size_tStepperSystemconst State &TimeTimeTimeObserverStepOverflowCheckerSecond version to solve the forwarding problem, can be called with Boost.Range as start_state. size_tStepperSystemState &TimeTimeTimeObserverintegrate_const without step overflow checker size_tStepperSystemconst State &TimeTimeTimeObserverSecond version to solve the forwarding problem, can be called with Boost.Range as start_state. size_tStepperSystemState &TimeTimeTimeintegrate_const without observer calls size_tStepperSystemconst State &TimeTimeTimeSecond version to solve the forwarding problem, can be called with Boost.Range as start_state.

TimeStepperSystemState &TimeTimesize_tObserverStepOverflowChecker TimeStepperSystemconst State &TimeTimesize_tObserverStepOverflowCheckerSolves the forwarding problem, can be called with Boost.Range as start_state. TimeStepperThe stepper to be used for numerical integration. SystemFunction/Functor defining the rhs of the ODE. State &The initial condition x0. TimeThe initial time t0. TimeThe time step between observer calls, not necessarily the time step of the integration. size_tNumber of steps to be performed ObserverFunction/Functor called at equidistant time intervals. The same function as above, but without checker. Integrates the ODE with constant step size.This function is similar to integrate_const. The observer is called at equidistant time intervals t0 + n*dt. If the Stepper is a normal stepper without step size control, dt is also used for the numerical scheme. If a ControlledStepper is provided, the algorithm might reduce the step size to meet the error bounds, but it is ensured that the observer is always called at equidistant time points t0 + n*dt. If a DenseOutputStepper is used, the step size also may vary and the dense output is used to call the observer at equidistant time points. The final integration time is always t0 + num_of_steps*dt. If a max_step_checker is provided as StepOverflowChecker, a no_progress_errror is thrown if too many steps (default: 500) are performed without progress, i.e. in between observer calls. If no checker is provided, no such overflow check is performed. The number of steps performed. TimeStepperSystemconst State &TimeTimesize_tObserverSolves the forwarding problem, can be called with Boost.Range as start_state. TimeStepperSystemState &TimeTimesize_tThe same function as above, but without observer calls. TimeStepperSystemconst State &TimeTimesize_tSolves the forwarding problem, can be called with Boost.Range as start_state.

size_tStepperSystemState &TimeIteratorTimeIteratorTimeObserverStepOverflowChecker size_tStepperSystemconst State &TimeIteratorTimeIteratorTimeObserverStepOverflowCheckerSolves the forwarding problem, can be called with Boost.Range as start_state. size_tStepperSystemState &const TimeRange &TimeObserverStepOverflowCheckerThe same function as above, but with the observation times given as range. size_tStepperSystemconst State &const TimeRange &TimeObserverStepOverflowCheckerSolves the forwarding problem, can be called with Boost.Range as start_state. size_tStepperThe stepper to be used for numerical integration. SystemFunction/Functor defining the rhs of the ODE. State &The initial condition x0. TimeIteratorIterator to the start time TimeIteratorIterator to the end time TimeThe time step between observer calls, not necessarily the time step of the integration. ObserverFunction/Functor called at equidistant time intervals. Integrates the ODE with observer calls at given time points. Integrates the ODE given by system using the given stepper. This function does observer calls at the subsequent time points given by the range times_start, times_end. If the stepper has not step size control, the step size might be reduced occasionally to ensure observer calls exactly at the time points from the given sequence. If the stepper is a ControlledStepper, the step size is adjusted to meet the error bounds, but also might be reduced occasionally to ensure correct observer calls. If a DenseOutputStepper is provided, the dense output functionality is used to call the observer at the given times. The end time of the integration is always *(end_time-1). If a max_step_checker is provided as StepOverflowChecker, a no_progress_error is thrown if too many steps (default: 500) are performed without progress, i.e. in between observer calls. If no checker is provided, no such overflow check is performed. The number of steps performed. size_tStepperSystemconst State &TimeIteratorTimeIteratorTimeObserverSolves the forwarding problem, can be called with Boost.Range as start_state. size_tStepperSystemState &const TimeRange &TimeObserverThe same function as above, but with the observation times given as range. size_tStepperSystemconst State &const TimeRange &TimeObserverSolves the forwarding problem, can be called with Boost.Range as start_state.

boost::numeric::odeint::max_step_checkerA class for performing overflow checks on the failed step count in step size adjustments. Used internally within the dense output stepper and integrate routines. voidvoidIncreases the counter and performs the iteration check. voidResets the max_step_checker by setting the internal counter to 0. const int500Construct the failed_step_checker. max_steps is the maximal number of iterations allowed before runtime_error is thrown. A class for performing overflow checks on the step count in integrate functions. Provide an instance of this class to integrate functions if you want to throw a runtime error if too many steps are performed without progress during the integrate routine. voidResets the max_step_checker by setting the internal counter to 0. voidvoidIncreases the counter and performs the iteration check. const int500Construct the max_step_checker. max_steps is the maximal number of iterations allowed before runtime_error is thrown.

ODE Iterator with adaptive step size. The value type of this iterator is the state type of the stepper. Implements an iterator representing the solution of an ODE from t_start to t_end evaluated at steps with an adaptive step size dt. After each iteration the iterator dereferences to the state x at the next time t+dt where dt is controlled by the stepper. This iterator can be used with ControlledSteppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_adaptive routine.adaptive_iterator is a model of single-pass iterator.The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time. StepperSystemState &time_typetime_typetime_type StepperSystemState & adaptive_iterator< Stepper, System, State >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. typename traits::time_type< Stepper >::typeThe initial time. typename traits::time_type< Stepper >::typeThe end time, at which the iteration should stop. typename traits::time_type< Stepper >::typeThe initial time step. Factory function for adaptive_iterator. Constructs a begin iterator. The adaptive iterator. adaptive_iterator< Stepper, System, State >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. Factory function for adaptive_iterator. Constructs a end iterator. The adaptive iterator. std::pair< adaptive_iterator< Stepper, System, State >, adaptive_iterator< Stepper, System, State > >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. typename traits::time_type< Stepper >::typeThe initial time. typename traits::time_type< Stepper >::typeThe end time, at which the iteration should stop. typename traits::time_type< Stepper >::typeThe initial time step. Factory function to construct a single pass range of adaptive iterators. A range is here a pair of adaptive_iterator. The adaptive range.

ODE Iterator with adaptive step size. The value type of this iterator is a std::pair containing state and time. Implements an iterator representing the solution of an ODE from t_start to t_end evaluated at steps with an adaptive step size dt. After each iteration the iterator dereferences to a pair containing state and time at the next time point t+dt where dt is controlled by the stepper. This iterator can be used with ControlledSteppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_adaptive routine.adaptive_iterator is a model of single-pass iterator.The value type of this iterator is a std::pair of state and time of the stepper. StepperSystemState &time_typetime_typetime_type StepperSystemState & adaptive_time_iterator< Stepper, System, State >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. adaptive_time_iterator stores a reference of s and changes its value during the iteration. typename traits::time_type< Stepper >::typeThe initial time. typename traits::time_type< Stepper >::typeThe end time, at which the iteration should stop. typename traits::time_type< Stepper >::typeThe initial time step. Factory function for adaptive_time_iterator. Constructs a begin iterator. The adaptive time iterator. adaptive_time_iterator< Stepper, System, State >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. adaptive_time_iterator stores a reference of s and changes its value during the iteration. Factory function for adaptive_time_iterator. Constructs a end iterator. The adaptive time iterator. std::pair< adaptive_time_iterator< Stepper, System, State >, adaptive_time_iterator< Stepper, System, State > >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. adaptive_time_iterator stores a reference of s and changes its value during the iteration. typename traits::time_type< Stepper >::typeThe initial time. typename traits::time_type< Stepper >::typeThe end time, at which the iteration should stop. typename traits::time_type< Stepper >::typeThe initial time step. Factory function to construct a single pass range of adaptive time iterators. A range is here a pair of adaptive_time_iterators. The adaptive time range.

ODE Iterator with constant step size. The value type of this iterator is the state type of the stepper. Implements an iterator representing the solution of an ODE from t_start to t_end evaluated at steps with constant step size dt. After each iteration the iterator dereferences to the state x at the next time t+dt. This iterator can be used with Steppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_const routine.const_step_iterator is a model of single-pass iterator.The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time. StepperSystemState &time_typetime_typetime_type StepperSystemState & const_step_iterator< Stepper, System, State >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_iterator stores a reference of s and changes its value during the iteration. typename traits::time_type< Stepper >::typeThe initial time. typename traits::time_type< Stepper >::typeThe end time, at which the iteration should stop. typename traits::time_type< Stepper >::typeThe initial time step. Factory function for const_step_iterator. Constructs a begin iterator. The const step iterator. const_step_iterator< Stepper, System, State >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_iterator stores a reference of s and changes its value during the iteration. Factory function for const_step_iterator. Constructs a end iterator. The const_step_iterator. std::pair< const_step_iterator< Stepper, System, State >, const_step_iterator< Stepper, System, State > >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_iterator store a reference of s and changes its value during the iteration. typename traits::time_type< Stepper >::typeThe initial time. typename traits::time_type< Stepper >::typeThe end time, at which the iteration should stop. typename traits::time_type< Stepper >::typeThe initial time step. Factory function to construct a single pass range of const step iterators. A range is here a pair of const_step_iterator. The const step range.

ODE Iterator with constant step size. The value type of this iterator is a std::pair containing state and time. Implements an iterator representing the solution of an ODE from t_start to t_end evaluated at steps with constant step size dt. After each iteration the iterator dereferences to a pair containing state and time at the next time point t+dt.. This iterator can be used with Steppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_const routine.const_step_time_iterator is a model of single-pass iterator.The value type of this iterator is a pair with the state type and time type of the stepper. StepperSystemState &time_typetime_typetime_type StepperSystemState & const_step_time_iterator< Stepper, System, State >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_time_iterator stores a reference of s and changes its value during the iteration. typename traits::time_type< Stepper >::typeThe initial time. typename traits::time_type< Stepper >::typeThe end time, at which the iteration should stop. typename traits::time_type< Stepper >::typeThe initial time step. Factory function for const_step_time_iterator. Constructs a begin iterator. The const step time iterator. const_step_time_iterator< Stepper, System, State >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_time_iterator store a reference of s and changes its value during the iteration. Factory function for const_step_time_iterator. Constructs a end iterator. The const step time iterator. std::pair< const_step_time_iterator< Stepper, System, State >, const_step_time_iterator< Stepper, System, State > >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_time_iterator stores a reference of s and changes its value during the iteration. typename traits::time_type< Stepper >::typetypename traits::time_type< Stepper >::typeThe end time, at which the iteration should stop. typename traits::time_type< Stepper >::typeThe initial time step. Factory function to construct a single pass range of const_step_time_iterator. A range is here a pair of const_step_time_iterator. The const step time range.

ODE Iterator with constant step size. The value type of this iterator is the state type of the stepper. Implements an iterator representing the solution of an ODE starting from t with n steps and a constant step size dt. After each iteration the iterator dereferences to the state x at the next time t+dt. This iterator can be used with Steppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_n_steps routine.n_step_iterator is a model of single-pass iterator.The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time. StepperSystemState &time_typetime_typesize_t StepperSystemState & n_step_iterator< Stepper, System, State >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_iterator stores a reference of s and changes its value during the iteration. typename traits::time_type< Stepper >::typeThe initial time. typename traits::time_type< Stepper >::typeThe initial time step. size_tThe number of steps to be executed. Factory function for n_step_iterator. Constructs a begin iterator. The n-step iterator. n_step_iterator< Stepper, System, State >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_iterator stores a reference of s and changes its value during the iteration. Factory function for n_step_iterator. Constructs an end iterator. The const_step_iterator. std::pair< n_step_iterator< Stepper, System, State >, n_step_iterator< Stepper, System, State > >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_iterator store a reference of s and changes its value during the iteration. typename traits::time_type< Stepper >::typeThe initial time. typename traits::time_type< Stepper >::typeThe initial time step. size_tThe number of steps to be executed. Factory function to construct a single pass range of n-step iterators. A range is here a pair of n_step_iterator. The n-step range.

ODE Iterator with constant step size. The value type of this iterator is a std::pair containing state and time. Implements an iterator representing the solution of an ODE starting from t with n steps and a constant step size dt. After each iteration the iterator dereferences to a pair of state and time at the next time t+dt. This iterator can be used with Steppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_n_steps routine.n_step_time_iterator is a model of single-pass iterator.The value type of this iterator is pair of state and time. StepperSystemState &time_typetime_typesize_t StepperSystemState & n_step_time_iterator< Stepper, System, State >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_iterator stores a reference of s and changes its value during the iteration. typename traits::time_type< Stepper >::typeThe initial time. typename traits::time_type< Stepper >::typeThe initial time step. size_tThe number of steps to be executed. Factory function for n_step_time_iterator. Constructs a begin iterator. The n-step iterator. n_step_time_iterator< Stepper, System, State >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_iterator stores a reference of s and changes its value during the iteration. Factory function for n_step_time_iterator. Constructs an end iterator. The const_step_iterator. std::pair< n_step_time_iterator< Stepper, System, State >, n_step_time_iterator< Stepper, System, State > >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_iterator store a reference of s and changes its value during the iteration. typename traits::time_type< Stepper >::typeThe initial time. typename traits::time_type< Stepper >::typeThe initial time step. size_tThe number of steps to be executed. Factory function to construct a single pass range of n-step iterators. A range is here a pair of n_step_time_iterator. The n-step range.

ODE Iterator with given evaluation points. The value type of this iterator is the state type of the stepper. Implements an iterator representing the solution of an ODE from *t_start to *t_end evaluated at time points given by the sequence t_start to t_end. t_start and t_end are iterators representing a sequence of time points where the solution of the ODE should be evaluated. After each iteration the iterator dereferences to the state x at the next time *t_start++ until t_end is reached. This iterator can be used with Steppers, ControlledSteppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_times routine.times_iterator is a model of single-pass iterator.The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time. StepperSystemState &TimeIteratorTimeIteratortime_type StepperSystemState & times_iterator< Stepper, System, State, TimeIterator >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_iterator stores a reference of s and changes its value during the iteration. TimeIteratorBegin iterator of the sequence of evaluation time points. TimeIteratorEnd iterator of the sequence of evaluation time points. typename traits::time_type< Stepper >::typeThe initial time step. Factory function for times_iterator. Constructs a begin iterator. The times iterator. times_iterator< Stepper, System, State, TimeIterator >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_iterator stores a reference of s and changes its value during the iteration. Factory function for times_iterator. Constructs an end iterator. This function needs the TimeIterator type specifically defined as a template parameter. The times iterator. std::pair< times_iterator< Stepper, System, State, TimeIterator >, times_iterator< Stepper, System, State, TimeIterator > >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_iterator store a reference of s and changes its value during the iteration. TimeIteratorBegin iterator of the sequence of evaluation time points. TimeIteratorEnd iterator of the sequence of evaluation time points. typename traits::time_type< Stepper >::typeThe initial time step. Factory function to construct a single pass range of times iterators. A range is here a pair of times_iterator. The times iterator range.

ODE Iterator with given evaluation points. The value type of this iterator is a std::pair containing state and time. Implements an iterator representing the solution of an ODE from *t_start to *t_end evaluated at time points given by the sequence t_start to t_end. t_start and t_end are iterators representing a sequence of time points where the solution of the ODE should be evaluated. After each iteration the iterator dereferences to a pair with the state and the time at the next evaluation point *t_start++ until t_end is reached. This iterator can be used with Steppers, ControlledSteppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_times routine.times_time_iterator is a model of single-pass iterator.The value type of this iterator is a pair of state and time type. StepperSystemState &TimeIteratorTimeIteratortime_type StepperSystemState & times_time_iterator< Stepper, System, State, TimeIterator >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_iterator stores a reference of s and changes its value during the iteration. TimeIteratorBegin iterator of the sequence of evaluation time points. TimeIteratorEnd iterator of the sequence of evaluation time points. typename traits::time_type< Stepper >::typeThe initial time step. Factory function for times_time_iterator. Constructs a begin iterator. The times_time iterator. times_time_iterator< Stepper, System, State, TimeIterator >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_iterator stores a reference of s and changes its value during the iteration. Factory function for times_time_iterator. Constructs an end iterator. This function needs the TimeIterator type specifically defined as a template parameter. The times_time iterator. std::pair< times_time_iterator< Stepper, System, State, TimeIterator >, times_time_iterator< Stepper, System, State, TimeIterator > >StepperThe stepper to use during the iteration. SystemThe system function (ODE) to solve. State &The initial state. const_step_iterator store a reference of s and changes its value during the iteration. TimeIteratorBegin iterator of the sequence of evaluation time points. TimeIteratorEnd iterator of the sequence of evaluation time points. typename traits::time_type< Stepper >::typeThe initial time step. Factory function to construct a single pass range of times_time iterators. A range is here a pair of times_iterator. The times_time iterator range.

algebra_stepper_base< Algebra, Operations >The Adams-Bashforth multistep algorithm. The Adams-Bashforth method is a multi-step algorithm with configurable step number. The step number is specified as template parameter Steps and it then uses the result from the previous Steps steps. See also en.wikipedia.org/wiki/Linear_multistep_method. Currently, a maximum of Steps=8 is supported. The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided.This class derives from algebra_base and inherits its interface via CRTP (current recurring template pattern). For more details see algebra_stepper_base. State state_wrapper< state_type > Value Deriv state_wrapper< deriv_type > Time Resizer stepper_tag InitializingStepper algebra_stepper_base< Algebra, Operations > algebra_stepper_base_type::algebra_type algebra_stepper_base_type::operations_type unsigned short unspecified const size_t const order_type order_typevoidReturns the order of the algorithm, which is equal to the number of steps. order of the method. voidSystemThe system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. StateInOut &The state of the ODE which should be solved. After calling do_step the result is updated in x. time_typeThe value of the time, at which the step should be performed. time_typeThe step size. This method performs one step. It transforms the result in-place. voidSystemconst StateInOut &time_typetime_typeSecond version to solve the forwarding problem, can be called with Boost.Range as StateInOut. voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. in is not modified in this method time_typeThe value of the time, at which the step should be performed. StateOut &The result of the step is written in out. time_typeThe step size. The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place. voidSystemconst StateIn &time_typeconst StateOut &time_typeSecond version to solve the forwarding problem, can be called with Boost.Range as StateOut. voidconst StateType &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. const step_storage_type &voidReturns the storage of intermediate results. The storage of intermediate results. step_storage_type &voidReturns the storage of intermediate results. The storage of intermediate results. voidExplicitStepperthe stepper used to fill the buffer of previous step results SystemThe system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. StateIn &The state of the ODE which should be solved. After calling do_step the result is updated in x. time_type &The value of the time, at which the step should be performed. time_typeThe step size. Initialized the stepper. Does Steps-1 steps with the explicit_stepper to fill the buffer. voidSystemThe system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. StateIn &The initial state of the ODE which should be solved, updated in this method. time_type &The initial value of the time, updated in this method. time_typeThe step size. Initialized the stepper. Does Steps-1 steps with an internal instance of InitializingStepper to fill the buffer. The state x and time t are updated to the values after Steps-1 initial steps. voidvoidResets the internal buffer of the stepper. boolvoidReturns true if the stepper has been initialized. bool true if stepper is initialized, false otherwise const initializing_stepper_type &voidReturns the internal initializing stepper instance. initializing_stepper initializing_stepper_type &voidReturns the internal initializing stepper instance. initializing_stepper const algebra_type &algebra_type()A copy of algebra is made and stored. Constructs the adams_bashforth class. This constructor can be used as a default constructor if the algebra has a default constructor. voidSystemconst StateIn &time_typeStateOut &time_type boolconst StateIn & boost::mpl::max::type< mpl::eval_if< mpl::equal_to< mpl::modulus< int_< N >, int_< 2 > >, int_< 0 > >, int_< N >, int_< N+1 > >::type, int_< 4 > >

The Adams-Bashforth-Moulton multistep algorithm. The Adams-Bashforth method is a multi-step predictor-corrector algorithm with configurable step number. The step number is specified as template parameter Steps and it then uses the result from the previous Steps steps. See also en.wikipedia.org/wiki/Linear_multistep_method. Currently, a maximum of Steps=8 is supported. The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided.This class derives from algebra_base and inherits its interface via CRTP (current recurring template pattern). For more details see algebra_stepper_base. State state_wrapper< state_type > Value Deriv state_wrapper< deriv_type > Time Algebra Operations Resizer stepper_tag InitializingStepper unsigned short const size_t const order_type order_typevoidReturns the order of the algorithm, which is equal to the number of steps+1. order of the method. voidSystemThe system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. StateInOut &The state of the ODE which should be solved. After calling do_step the result is updated in x. time_typeThe value of the time, at which the step should be performed. time_typeThe step size. This method performs one step. It transforms the result in-place. voidSystemconst StateInOut &time_typetime_typeSecond version to solve the forwarding problem, can be called with Boost.Range as StateInOut. voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. in is not modified in this method time_typeThe value of the time, at which the step should be performed. const StateOut &The result of the step is written in out. time_typeThe step size. The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place. voidSystemconst StateIn &time_typeStateOut &time_typeSecond version to solve the forwarding problem, can be called with Boost.Range as StateOut. voidconst StateType &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. voidExplicitStepperthe stepper used to fill the buffer of previous step results SystemThe system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. StateIn &The initial state of the ODE which should be solved, updated after in this method. time_type &The initial time, updated in this method. time_typeThe step size. Initialized the stepper. Does Steps-1 steps with the explicit_stepper to fill the buffer. The state x and time t are updated to the values after Steps-1 initial steps. voidSystemThe system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. StateIn &The state of the ODE which should be solved. After calling do_step the result is updated in x. time_type &The value of the time, at which the step should be performed. time_typeThe step size. Initialized the stepper. Does Steps-1 steps using the standard initializing stepper of the underlying adams_bashforth stepper. voidvoidResets the internal buffers of the stepper. voidConstructs the adams_bashforth class. const algebra_type &A copy of algebra is made and stored. Constructs the adams_bashforth class. This constructor can be used as a default constructor if the algebra has a default constructor. voidSystemStateInOut &time_typetime_type voidSystemStateIn const &time_typeStateInOut &time_type boolconst StateIn &

State state_wrapper< state_type > Value Deriv state_wrapper< deriv_type > Time Algebra Operations Resizer stepper_tag adams_moulton< Steps, State, Value, Deriv, Time, Algebra, Operations, Resizer > unsigned short unspecified const size_t const order_type order_typevoid voidSystemStateInOut &StateIn const &time_typetime_typeconst ABBuf & voidSystemconst StateInOut &StateIn const &time_typetime_typeconst ABBuf & voidSystemconst StateIn &const PredIn &time_typeStateOut &time_typeconst ABBuf & voidSystemconst StateIn &const PredIn &time_typeconst StateOut &time_typeconst ABBuf & voidconst StateType & algebra_type & const algebra_type & algebra_type & adams_moulton &const adams_moulton & voidSystemconst StateIn &const PredIn &time_typeStateOut &time_typeconst ABBuf & boolconst StateIn &

algebra_stepper_base< Algebra, Operations >unsigned short State Value Deriv Time state_wrapper< state_type > state_wrapper< deriv_type > algebra_stepper_base< Algebra, Operations > algebra_stepper_base_type::algebra_type algebra_stepper_base_type::operations_type Resizer error_stepper_tag unspecified adaptive_adams_bashforth_moulton< Steps, State, Value, Deriv, Time, Algebra, Operations, Resizer > const size_t const order_type order_type order_type order_type voidSystemstate_type &time_typetime_type voidSystemconst state_type &time_typestate_type &time_type voidSystemstate_type &time_typetime_typestate_type & voidSystemconst state_type &time_typestate_type &time_typestate_type & voidExplicitStepperSystemstate_type &time_type &time_type voidSystemstate_type &time_type &time_type voidSystemconst state_type &time_typestate_type &time_type &state_type & const coeff_type & coeff_type & void const deriv_type & const algebra_type &algebra_type() boolconst StateType & boolconst StateType & boolconst StateType &

The Bulirsch-Stoer algorithm. The Bulirsch-Stoer is a controlled stepper that adjusts both step size and order of the method. The algorithm uses the modified midpoint and a polynomial extrapolation compute the solution. State Value Deriv Time Algebra Operations Resizer const size_t controlled_step_resultSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. StateInOut &The state of the ODE which should be solved. Overwritten if the step is successful. time_type &The value of the time. Updated if the step is successful. time_type &The step size. Updated. Tries to perform one step. This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required. success if the step was accepted, fail otherwise. controlled_step_resultSystemconst StateInOut &time_type &time_type &Second version to solve the forwarding problem, can be used with Boost.Range as StateInOut. controlled_step_resultSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. StateInOut &The state of the ODE which should be solved. Overwritten if the step is successful. const DerivIn &The derivative of state. time_type &The value of the time. Updated if the step is successful. time_type &The step size. Updated. Tries to perform one step. This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required. success if the step was accepted, fail otherwise. boost::disable_if< boost::is_same< StateIn, time_type >, controlled_step_result >::typeSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. time_type &The value of the time. Updated if the step is successful. StateOut &Used to store the result of the step. time_type &The step size. Updated. Tries to perform one step. This method is disabled if state_type=time_type to avoid ambiguity. This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required. success if the step was accepted, fail otherwise. controlled_step_resultSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. const DerivIn &The derivative of state. time_type &The value of the time. Updated if the step is successful. StateOut &Used to store the result of the step. time_type &The step size. Updated. Tries to perform one step. This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required. success if the step was accepted, fail otherwise. voidResets the internal state of the stepper. voidconst StateIn &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. value_type1E-6Absolute tolerance level. value_type1E-6Relative tolerance level. value_type1.0Factor for the weight of the state. value_type1.0Factor for the weight of the derivative. time_typestatic_cast< time_type >(0)Constructs the bulirsch_stoer class, including initialization of the error bounds. boolconst StateIn & boolconst StateIn & boolconst StateIn & controlled_step_resultSystemStateInOut &time_type &time_type & voidsize_tstate_table_type &const value_matrix &StateInOut & time_typetime_typevalue_typesize_t controlled_step_resultsize_tconst inv_time_vector &const time_vector &time_type & boolsize_t boolvalue_typesize_t

The Bulirsch-Stoer algorithm. The Bulirsch-Stoer is a controlled stepper that adjusts both step size and order of the method. The algorithm uses the modified midpoint and a polynomial extrapolation compute the solution. This class also provides dense output facility. State Value Deriv Time Algebra Operations Resizer dense_output_stepper_tag const size_t controlled_step_resultSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. const DerivIn &The derivative of state. time_type &The value of the time. Updated if the step is successful. StateOut &Used to store the result of the step. DerivOut &time_type &The step size. Updated. Tries to perform one step. This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required. success if the step was accepted, fail otherwise. voidconst StateType &The initial state. const time_type &The initial time. const time_type &The initial time step. Initializes the dense output stepper. std::pair< time_type, time_type >SystemThe system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. Does one time step. This is the main method that should be used to integrate an ODE with this stepper. initialize has to be called before using this method to set the initial conditions x,t and the stepsize. Pair with start and end time of the integration step. voidtime_typeThe time at which the solution should be calculated, has to be in the current time interval. StateOut &The output variable where the result is written into. Calculates the solution at an intermediate point within the last step. const state_type &voidReturns the current state of the solution. The current state of the solution x(t). time_typevoidReturns the current time of the solution. The current time of the solution t. const state_type &voidReturns the last state of the solution. The last state of the solution x(t-dt). time_typevoidReturns the last time of the solution. The last time of the solution t-dt. time_typevoidReturns the current step size. The current step size. voidResets the internal state of the stepper. voidconst StateIn &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. value_type1E-6Absolute tolerance level. value_type1E-6Relative tolerance level. value_type1.0Factor for the weight of the state. value_type1.0Factor for the weight of the derivative. time_typestatic_cast< time_type >(0)boolfalseSet true to additionally control the error of the interpolation. Constructs the bulirsch_stoer class, including initialization of the error bounds. voidsize_tStateVector &const value_matrix &StateInOut &size_t0 voidsize_tStateVector &const value_matrix &size_t0 time_typetime_typevalue_typesize_t boolsize_t boolvalue_typesize_t value_typeintconst StateIn1 &const DerivIn1 &const StateIn2 &const DerivIn2 &time_type voidsize_tsize_tvalue_typeconst DerivIn & voidtime_typeStateOut & boolconst StateIn & state_type &void const state_type &void state_type &void const state_type &void deriv_type &void const deriv_type &void deriv_type &void const deriv_type &void voidvoid

ErrorStepper stepper_type::state_type stepper_type::value_type stepper_type::deriv_type stepper_type::time_type stepper_type::algebra_type stepper_type::operations_type Resizer StepAdjuster OrderAdjuster controlled_stepper_tag stepper_type::wrapped_state_type stepper_type::wrapped_deriv_type boost::array< wrapped_state_type, 4 > stepper_type::coeff_type controlled_adams_bashforth_moulton< ErrorStepper, StepAdjuster, OrderAdjuster, Resizer > const stepper_type::order_type voidExplicitStepperSystemstate_type &time_type &time_type voidSystemstate_type &time_type &time_type voidExplicitStepperSystemstate_type &time_type &time_type & controlled_step_resultSystemstate_type &time_type &time_type & controlled_step_resultSystemconst state_type &time_type &state_type &time_type & void step_adjuster_typestep_adjuster_type() boolconst StateType & boolconst StateType & boolconst StateType & State Value state_wrapper< state_type > Algebra size_tsize_tsize_tboost::array< wrapped_state_type, 4 > & const algebra_type &algebra_type()

ErrorStepperErrorCheckerStepAdjusterResizerexplicit_error_stepper_fsal_tagImplements step size control for Runge-Kutta FSAL steppers with error estimation. This class implements the step size control for FSAL Runge-Kutta steppers with error estimation. ErrorStepper stepper_type::state_type stepper_type::value_type stepper_type::deriv_type stepper_type::time_type stepper_type::algebra_type stepper_type::operations_type Resizer ErrorChecker StepAdjuster explicit_controlled_stepper_fsal_tag controlled_step_resultSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. StateInOut &The state of the ODE which should be solved. Overwritten if the step is successful. time_type &The value of the time. Updated if the step is successful. time_type &The step size. Updated. Tries to perform one step. This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. success if the step was accepted, fail otherwise. controlled_step_resultSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateInOut &The state of the ODE which should be solved. Overwritten if the step is successful. Can be a boost range. time_type &The value of the time. Updated if the step is successful. time_type &The step size. Updated. Tries to perform one step. Solves the forwarding problem and allows for using boost range as state_type. This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. success if the step was accepted, fail otherwise. boost::disable_if< boost::is_same< StateIn, time_type >, controlled_step_result >::typeSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. time_type &The value of the time. Updated if the step is successful. StateOut &Used to store the result of the step. time_type &The step size. Updated. Tries to perform one step. This method is disabled if state_type=time_type to avoid ambiguity. This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. success if the step was accepted, fail otherwise. controlled_step_resultSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. StateInOut &The state of the ODE which should be solved. Overwritten if the step is successful. DerivInOut &The derivative of state. time_type &The value of the time. Updated if the step is successful. time_type &The step size. Updated. Tries to perform one step. This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. success if the step was accepted, fail otherwise. controlled_step_resultSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. const DerivIn &time_type &The value of the time. Updated if the step is successful. StateOut &Used to store the result of the step. DerivOut &time_type &The step size. Updated. Tries to perform one step. This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. success if the step was accepted, fail otherwise. voidvoidResets the internal state of the underlying FSAL stepper. voidconst DerivIn &The initial derivative of the ODE. Initializes the internal state storing an internal copy of the derivative. voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The initial state of the ODE which should be solved. time_typeThe initial time. Initializes the internal state storing an internal copy of the derivative. boolvoidReturns true if the stepper has been initialized, false otherwise. true, if the stepper has been initialized, false otherwise. voidconst StateType &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. stepper_type &voidReturns the instance of the underlying stepper. The instance of the underlying stepper. const stepper_type &voidReturns the instance of the underlying stepper. The instance of the underlying stepper. const error_checker_type &error_checker_type()An instance of the error checker. const step_adjuster_type &step_adjuster_type()const stepper_type &stepper_type()An instance of the underlying stepper. Constructs the controlled Runge-Kutta stepper. boolconst StateIn & boolconst StateIn & boolconst StateIn & boolconst StateIn & controlled_step_resultSystemStateInOut &time_type &time_type & ErrorStepperErrorCheckerStepAdjusterResizerexplicit_error_stepper_tagImplements step size control for Runge-Kutta steppers with error estimation. This class implements the step size control for standard Runge-Kutta steppers with error estimation. ErrorStepper stepper_type::state_type stepper_type::value_type stepper_type::deriv_type stepper_type::time_type stepper_type::algebra_type stepper_type::operations_type Resizer ErrorChecker StepAdjuster explicit_controlled_stepper_tag controlled_step_resultSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. StateInOut &The state of the ODE which should be solved. Overwritten if the step is successful. time_type &The value of the time. Updated if the step is successful. time_type &The step size. Updated. Tries to perform one step. This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. success if the step was accepted, fail otherwise. controlled_step_resultSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateInOut &The state of the ODE which should be solved. Overwritten if the step is successful. Can be a boost range. time_type &The value of the time. Updated if the step is successful. time_type &The step size. Updated. Tries to perform one step. Solves the forwarding problem and allows for using boost range as state_type. This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. success if the step was accepted, fail otherwise. controlled_step_resultSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. StateInOut &The state of the ODE which should be solved. Overwritten if the step is successful. const DerivIn &The derivative of state. time_type &The value of the time. Updated if the step is successful. time_type &The step size. Updated. Tries to perform one step. This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. success if the step was accepted, fail otherwise. boost::disable_if< boost::is_same< StateIn, time_type >, controlled_step_result >::typeSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. time_type &The value of the time. Updated if the step is successful. StateOut &Used to store the result of the step. time_type &The step size. Updated. Tries to perform one step. This method is disabled if state_type=time_type to avoid ambiguity. This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. success if the step was accepted, fail otherwise. controlled_step_resultSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. const DerivIn &The derivative of state. time_type &The value of the time. Updated if the step is successful. StateOut &Used to store the result of the step. time_type &The step size. Updated. Tries to perform one step. This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. success if the step was accepted, fail otherwise. voidconst StateType &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. stepper_type &voidReturns the instance of the underlying stepper. The instance of the underlying stepper. const stepper_type &voidReturns the instance of the underlying stepper. The instance of the underlying stepper. const error_checker_type &error_checker_type()An instance of the error checker. const step_adjuster_type &step_adjuster_type()const stepper_type &stepper_type()An instance of the underlying stepper. Constructs the controlled Runge-Kutta stepper. controlled_step_resultSystemStateInOut &time_type &time_type & boolconst StateIn & boolconst StateIn & boolconst StateIn & The default error checker to be used with Runge-Kutta error steppers. This class provides the default mechanism to compare the error estimates reported by Runge-Kutta error steppers with user defined error bounds. It is used by the controlled_runge_kutta steppers. Value Algebra Operations value_typeconst State &const Deriv &Err &Time value_typealgebra_type &const State &const Deriv &Err &Time value_typestatic_cast< value_type >(1.0e-6)value_typestatic_cast< value_type >(1.0e-6)value_typestatic_cast< value_type >(1)value_typestatic_cast< value_type >(1) Time Value time_typetime_typeconst value_typeconst int time_typetime_typevalue_typeconst int boolconst time_type time_type const time_typestatic_cast< time_type >(0)

The trial step was successful, hence the state and the time have been advanced. The step was not successful and might possibly be repeated with a small step size. Enum representing the return values of the controlled steppers.

Stepperexplicit_controlled_stepper_fsal_tagThe class representing dense-output Runge-Kutta steppers with FSAL property. The interface is the same as for dense_output_runge_kutta< Stepper , stepper_tag >. This class provides dense output functionality based on methods with step size controlled Stepper controlled_stepper_type::stepper_type stepper_type::state_type stepper_type::wrapped_state_type stepper_type::value_type stepper_type::deriv_type stepper_type::wrapped_deriv_type stepper_type::time_type stepper_type::algebra_type stepper_type::operations_type stepper_type::resizer_type dense_output_stepper_tag dense_output_runge_kutta< Stepper > voidconst StateType &time_typetime_type std::pair< time_type, time_type >System voidtime_typeStateOut & voidtime_typeconst StateOut & boolconst StateIn & voidconst StateType & const state_type &void time_typevoid const state_type &void time_typevoid time_typevoid const controlled_stepper_type &controlled_stepper_type() state_type &void const state_type &void state_type &void const state_type &void deriv_type &void const deriv_type &void deriv_type &void const deriv_type &void voidvoid Stepperstepper_tagThe class representing dense-output Runge-Kutta steppers. In this stepper, the initialize method has to be called before using the do_step method. The dense-output functionality allows to interpolate the solution between subsequent integration points using intermediate results obtained during the computation. This version works based on a normal stepper without step-size control. Stepper stepper_type::state_type stepper_type::wrapped_state_type stepper_type::value_type stepper_type::deriv_type stepper_type::wrapped_deriv_type stepper_type::time_type stepper_type::algebra_type stepper_type::operations_type stepper_type::resizer_type dense_output_stepper_tag dense_output_runge_kutta< Stepper > voidconst StateType &The initial state of the ODE which should be solved. time_typeThe initial time, at which the step should be performed. time_typeThe step size. Initializes the stepper. Has to be called before do_step can be used to set the initial conditions and the step size. std::pair< time_type, time_type >SystemThe system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept. Does one time step. initialize has to be called before using this method to set the initial conditions x,t and the stepsize. Pair with start and end time of the integration step. voidtime_typeThe time at which the solution should be calculated, has to be in the current time interval. StateOut &The output variable where the result is written into. Calculates the solution at an intermediate point. voidtime_typeThe time at which the solution should be calculated, has to be in the current time interval. const StateOut &The output variable where the result is written into, can be a boost range. Calculates the solution at an intermediate point. Solves the forwarding problem. voidconst StateType &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. const state_type &voidReturns the current state of the solution. The current state of the solution x(t). time_typevoidReturns the current time of the solution. The current time of the solution t. const state_type &voidReturns the last state of the solution. The last state of the solution x(t-dt). time_typevoidReturns the last time of the solution. The last time of the solution t-dt. time_typevoidReturns the current time step. dt. const stepper_type &stepper_type()An instance of the underlying stepper. Constructs the dense_output_runge_kutta class. An instance of the underlying stepper can be provided. state_type &void const state_type &void state_type &void const state_type &void voidvoid boolconst StateIn &

explicit_stepper_baseAn implementation of the Euler method. The Euler method is a very simply solver for ordinary differential equations. This method should not be used for real applications. It is only useful for demonstration purposes. Step size control is not provided but trivial continuous output is available.This class derives from explicit_stepper_base and inherits its interface via CRTP (current recurring template pattern), see explicit_stepper_base explicit_stepper_base< euler< ... >,... > stepper_base_type::state_type stepper_base_type::value_type stepper_base_type::deriv_type stepper_base_type::time_type stepper_base_type::algebra_type stepper_base_type::operations_type stepper_base_type::resizer_type voidSystemconst StateIn &The state of the ODE which should be solved. in is not modified in this method const DerivIn &The derivative of x at t. time_typeStateOut &The result of the step is written in out. time_typeThe step size. This method performs one step. The derivative dxdt of in at the time t is passed to the method. The result is updated out of place, hence the input is in in and the output in out. Access to this step functionality is provided by explicit_stepper_base and do_step_impl should not be called directly. voidStateOut &time_typeconst StateIn1 &time_typeconst StateIn2 &time_typeThis method is used for continuous output and it calculates the state x at a time t from the knowledge of two states old_state and current_state at time points t_old and t_new. voidconst StateType &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. const algebra_type &algebra_type()A copy of algebra is made and stored inside explicit_stepper_base. Constructs the euler class. This constructor can be used as a default constructor of the algebra has a default constructor.

explicit_error_stepper_baseA generic implementation of explicit Runge-Kutta algorithms with error estimation. This class is as a base class for all explicit Runge-Kutta steppers with error estimation. This class implements the explicit Runge-Kutta algorithms with error estimation in a generic way. The Butcher tableau is passed to the stepper which constructs the stepper scheme with the help of a template-metaprogramming algorithm. ToDo : Add example!This class derives explicit_error_stepper_base which provides the stepper interface. explicit_stepper_base< ... > stepper_base_type::state_type stepper_base_type::wrapped_state_type stepper_base_type::value_type stepper_base_type::deriv_type stepper_base_type::wrapped_deriv_type stepper_base_type::time_type stepper_base_type::algebra_type stepper_base_type::operations_type stepper_base_type::resizer_type unspecified rk_algorithm_type::coef_a_type rk_algorithm_type::coef_b_type rk_algorithm_type::coef_c_type const size_t voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. in is not modified in this method const DerivIn &The derivative of x at t. time_typeThe value of the time, at which the step should be performed. StateOut &The result of the step is written in out. time_typeThe step size. Err &The result of the error estimation is written in xerr. This method performs one step. The derivative dxdt of in at the time t is passed to the method. The result is updated out-of-place, hence the input is in in and the output in out. Futhermore, an estimation of the error is stored in xerr. do_step_impl is used by explicit_error_stepper_base. voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. in is not modified in this method const DerivIn &The derivative of x at t. time_typeThe value of the time, at which the step should be performed. StateOut &The result of the step is written in out. time_typeThe step size. This method performs one step. The derivative dxdt of in at the time t is passed to the method. The result is updated out-of-place, hence the input is in in and the output in out. Access to this step functionality is provided by explicit_stepper_base and do_step_impl should not be called directly. voidconst StateIn &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. const coef_a_type &Triangular matrix of parameters b in the Butcher tableau. const coef_b_type &Last row of the butcher tableau. const coef_b_type &Parameters for lower-order evaluation to estimate the error. const coef_c_type &Parameters to calculate the time points in the Butcher tableau. const algebra_type &algebra_type()A copy of algebra is made and stored inside explicit_stepper_base. Constructs the explicit_error_generik_rk class with the given parameters a, b, b2 and c. See examples section for details on the coefficients. boolconst StateIn &

explicit_stepper_baseA generic implementation of explicit Runge-Kutta algorithms. This class is as a base class for all explicit Runge-Kutta steppers. This class implements the explicit Runge-Kutta algorithms without error estimation in a generic way. The Butcher tableau is passed to the stepper which constructs the stepper scheme with the help of a template-metaprogramming algorithm. ToDo : Add example!This class derives explicit_stepper_base which provides the stepper interface. explicit_stepper_base< ... > stepper_base_type::state_type stepper_base_type::wrapped_state_type stepper_base_type::value_type stepper_base_type::deriv_type stepper_base_type::wrapped_deriv_type stepper_base_type::time_type stepper_base_type::algebra_type stepper_base_type::operations_type stepper_base_type::resizer_type unspecified rk_algorithm_type::coef_a_type rk_algorithm_type::coef_b_type rk_algorithm_type::coef_c_type voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. in is not modified in this method const DerivIn &The derivative of x at t. time_typeThe value of the time, at which the step should be performed. StateOut &The result of the step is written in out. time_typeThe step size. This method performs one step. The derivative dxdt of in at the time t is passed to the method. The result is updated out of place, hence the input is in in and the output in out. Access to this step functionality is provided by explicit_stepper_base and do_step_impl should not be called directly. voidconst StateIn &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. const coef_a_type &Triangular matrix of parameters b in the Butcher tableau. const coef_b_type &Last row of the butcher tableau. const coef_c_type &Parameters to calculate the time points in the Butcher tableau. const algebra_type &algebra_type()A copy of algebra is made and stored inside explicit_stepper_base. Constructs the explicit_generic_rk class. See examples section for details on the coefficients. boolconst StateIn &

explicit_error_stepper_baseExtrapolation stepper with configurable order, and error estimation. The extrapolation stepper is a stepper with error estimation and configurable order. The order is given as template parameter and needs to be an odd number. The stepper is based on several executions of the modified midpoint method and a Richardson extrapolation. This is essentially the same technique as for bulirsch_stoer, but without the variable order.The Order parameter has to be an even number greater 2. explicit_error_stepper_base< extrapolation_stepper< ... >,... > stepper_base_type::state_type stepper_base_type::value_type stepper_base_type::deriv_type stepper_base_type::time_type stepper_base_type::algebra_type stepper_base_type::operations_type stepper_base_type::resizer_type unsigned short const order_type const order_type const order_type const size_t ((Order % 2)==0) &&(Order > 2)"extrapolation_stepper requires even Order larger than 2" boolconst StateIn & boolconst StateIn & voidsize_tstate_table_type &const value_matrix &StateInOut & voidSystemconst StateIn &const DerivIn &time_typeStateOut &time_typeErr & voidSystemStateInOut &const DerivIn &time_typetime_typeErr & voidSystemconst StateIn &const DerivIn &time_typeStateOut &time_type voidSystemStateInOut &const DerivIn &time_typetime_type voidSystemStateInOut &const DerivIn &time_typetime_type voidSystemconst StateIn &const DerivIn &time_typeStateOut &time_type voidconst StateIn & const algebra_type &algebra_type()

ValueType value_type boost::numeric::ublas::vector< value_type > state_wrapper< state_type > state_type state_wrapper< deriv_type > boost::numeric::ublas::matrix< value_type > state_wrapper< matrix_type > boost::numeric::ublas::permutation_matrix< size_t > state_wrapper< pmatrix_type > Resizer stepper_tag implicit_euler< ValueType, Resizer > voidSystemstate_type &time_typetime_type voidconst StateType & value_type1E-6 boolconst StateIn & voidstate_type &matrix_type &

explicit_stepper_baseImplementation of the modified midpoint method with a configurable number of intermediate steps. This class is used by the Bulirsch-Stoer algorithm and is not meant for direct usage. explicit_stepper_base< modified_midpoint< State, Value, Deriv, Time, Algebra, Operations, Resizer >, 2, State, Value, Deriv, Time, Algebra, Operations, Resizer > stepper_base_type::state_type stepper_base_type::wrapped_state_type stepper_base_type::value_type stepper_base_type::deriv_type stepper_base_type::wrapped_deriv_type stepper_base_type::time_type stepper_base_type::algebra_type stepper_base_type::operations_type stepper_base_type::resizer_type stepper_base_type::stepper_type voidSystemconst StateIn &const DerivIn &time_typeStateOut &time_type voidunsigned short unsigned shortvoid voidconst StateIn & unsigned short2const algebra_type &algebra_type() boolconst StateIn & Implementation of the modified midpoint method with a configurable number of intermediate steps. This class is used by the dense output Bulirsch-Stoer algorithm and is not meant for direct usage. This stepper is for internal use only and does not meet any stepper concept. State Value Deriv Time Algebra Operations Resizer state_wrapper< state_type > state_wrapper< deriv_type > modified_midpoint_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer > std::vector< wrapped_deriv_type > voidSystemconst StateIn &const DerivIn &time_typeStateOut &time_typestate_type &deriv_table_type & voidunsigned short unsigned shortvoid boolconst StateIn & voidconst StateIn & unsigned short2const algebra_type &algebra_type()

Value unsigned short const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const value_type const order_type const order_type void Value boost::numeric::ublas::vector< value_type > state_type value_type boost::numeric::ublas::matrix< value_type > boost::numeric::ublas::permutation_matrix< size_t > Resizer Coefficients stepper_tag unsigned short state_wrapper< state_type > state_wrapper< deriv_type > state_wrapper< matrix_type > state_wrapper< pmatrix_type > rosenbrock4< Value, Coefficients, Resizer > const order_type const order_type order_type voidSystemconst state_type &time_typestate_type &time_typestate_type & voidSystemstate_type &time_typetime_typestate_type & voidSystemconst state_type &time_typestate_type &time_type voidSystemstate_type &time_typetime_type void voidtime_typestate_type &const state_type &time_typeconst state_type &time_type voidconst StateType & void boolconst StateIn & boolconst StateIn &

Stepper stepper_type::value_type stepper_type::state_type stepper_type::wrapped_state_type stepper_type::time_type stepper_type::deriv_type stepper_type::wrapped_deriv_type stepper_type::resizer_type controlled_stepper_tag rosenbrock4_controller< Stepper > value_typeconst state_type &const state_type &const state_type & value_typevoid boost::numeric::odeint::controlled_step_resultSystemstate_type &time_type &time_type & boost::numeric::odeint::controlled_step_resultSystemconst state_type &time_type &state_type &time_type & voidconst StateType & stepper_type &void const stepper_type &void value_type1.0e-6value_type1.0e-6const stepper_type &stepper_type() value_typevalue_typetime_typeconst stepper_type &stepper_type() boolconst StateIn & boolconst StateIn &

ControlledStepper unwrap_reference< controlled_stepper_type >::type unwrapped_controlled_stepper_type::stepper_type stepper_type::value_type stepper_type::state_type stepper_type::wrapped_state_type stepper_type::time_type stepper_type::deriv_type stepper_type::wrapped_deriv_type stepper_type::resizer_type dense_output_stepper_tag rosenbrock4_dense_output< ControlledStepper > voidconst StateType &time_typetime_type std::pair< time_type, time_type >System voidtime_typeStateOut & voidtime_typeconst StateOut & voidconst StateType & const state_type &void time_typevoid const state_type &void time_typevoid time_typevoid const controlled_stepper_type &controlled_stepper_type() state_type &void const state_type &void state_type &void const state_type &void voidvoid boolconst StateIn &

boost::numeric::odeint::explicit_generic_rk< StageCount, Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >The classical Runge-Kutta stepper of fourth order. The Runge-Kutta method of fourth order is one standard method for solving ordinary differential equations and is widely used, see also en.wikipedia.org/wiki/Runge-Kutta_methods The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided.This class derives from explicit_stepper_base and inherits its interface via CRTP (current recurring template pattern). Furthermore, it derivs from explicit_generic_rk which is a generic Runge-Kutta algorithm. For more details see explicit_stepper_base and explicit_generic_rk. stepper_base_type::state_type stepper_base_type::value_type stepper_base_type::deriv_type stepper_base_type::time_type stepper_base_type::algebra_type stepper_base_type::operations_type stepper_base_type::resizer_type voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. in is not modified in this method const DerivIn &The derivative of x at t. time_typeThe value of the time, at which the step should be performed. StateOut &The result of the step is written in out. time_typeThe step size. This method performs one step. The derivative dxdt of in at the time t is passed to the method. The result is updated out of place, hence the input is in in and the output in out. Access to this step functionality is provided by explicit_stepper_base and do_step_impl should not be called directly. voidconst StateIn &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. const algebra_type &algebra_type()A copy of algebra is made and stored inside explicit_stepper_base. Constructs the runge_kutta4 class. This constructor can be used as a default constructor if the algebra has a default constructor.

explicit_stepper_baseThe classical Runge-Kutta stepper of fourth order. The Runge-Kutta method of fourth order is one standard method for solving ordinary differential equations and is widely used, see also en.wikipedia.org/wiki/Runge-Kutta_methods The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided. This class implements the method directly, hence the generic Runge-Kutta algorithm is not used.This class derives from explicit_stepper_base and inherits its interface via CRTP (current recurring template pattern). For more details see explicit_stepper_base. explicit_stepper_base< runge_kutta4_classic< ... >,... > stepper_base_type::state_type stepper_base_type::value_type stepper_base_type::deriv_type stepper_base_type::time_type stepper_base_type::algebra_type stepper_base_type::operations_type stepper_base_type::resizer_type voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. in is not modified in this method const DerivIn &The derivative of x at t. time_typeThe value of the time, at which the step should be performed. StateOut &The result of the step is written in out. time_typeThe step size. This method performs one step. The derivative dxdt of in at the time t is passed to the method. The result is updated out of place, hence the input is in in and the output in out. Access to this step functionality is provided by explicit_stepper_base and do_step_impl should not be called directly. voidconst StateType &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. const algebra_type &algebra_type()A copy of algebra is made and stored inside explicit_stepper_base. Constructs the runge_kutta4_classic class. This constructor can be used as a default constructor if the algebra has a default constructor. boolconst StateIn &

boost::numeric::odeint::explicit_error_generic_rk< StageCount, Order, StepperOrder, ErrorOrder, State, Value, Deriv, Time, Algebra, Operations, Resizer >The Runge-Kutta Cash-Karp method. The Runge-Kutta Cash-Karp method is one of the standard methods for solving ordinary differential equations, see en.wikipedia.org/wiki/Cash-Karp_methods. The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is not available for this method.This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern). Furthermore, it derivs from explicit_error_generic_rk which is a generic Runge-Kutta algorithm with error estimation. For more details see explicit_error_stepper_base and explicit_error_generic_rk. stepper_base_type::state_type stepper_base_type::value_type stepper_base_type::deriv_type stepper_base_type::time_type stepper_base_type::algebra_type stepper_base_type::operations_type stepper_base_type::resizer_type voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. in is not modified in this method const DerivIn &The derivative of x at t. time_typeThe value of the time, at which the step should be performed. StateOut &The result of the step is written in out. time_typeThe step size. Err &The result of the error estimation is written in xerr. This method performs one step. The derivative dxdt of in at the time t is passed to the method. The result is updated out-of-place, hence the input is in in and the output in out. Futhermore, an estimation of the error is stored in xerr. do_step_impl is used by explicit_error_stepper_base. voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. in is not modified in this method const DerivIn &The derivative of x at t. time_typeThe value of the time, at which the step should be performed. StateOut &The result of the step is written in out. time_typeThe step size. This method performs one step. The derivative dxdt of in at the time t is passed to the method. The result is updated out-of-place, hence the input is in in and the output in out. Access to this step functionality is provided by explicit_stepper_base and do_step_impl should not be called directly. voidconst StateIn &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. const algebra_type &algebra_type()A copy of algebra is made and stored inside explicit_stepper_base. Constructs the runge_kutta_cash_karp54 class. This constructor can be used as a default constructor if the algebra has a default constructor.

explicit_error_stepper_baseThe Runge-Kutta Cash-Karp method implemented without the generic Runge-Kutta algorithm. The Runge-Kutta Cash-Karp method is one of the standard methods for solving ordinary differential equations, see en.wikipedia.org/wiki/Cash-Karp_method. The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is not available for this method.This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern). This class implements the method directly, hence the generic Runge-Kutta algorithm is not used. explicit_error_stepper_base< runge_kutta_cash_karp54_classic< ... >,... > stepper_base_type::state_type stepper_base_type::value_type stepper_base_type::deriv_type stepper_base_type::time_type stepper_base_type::algebra_type stepper_base_type::operations_type stepper_base_type::resizer_type voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. in is not modified in this method const DerivIn &The derivative of x at t. time_typeThe value of the time, at which the step should be performed. StateOut &The result of the step is written in out. time_typeThe step size. Err &The result of the error estimation is written in xerr. This method performs one step. The derivative dxdt of in at the time t is passed to the method. The result is updated out-of-place, hence the input is in in and the output in out. Futhermore, an estimation of the error is stored in xerr. Access to this step functionality is provided by explicit_error_stepper_base and do_step_impl should not be called directly. voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. in is not modified in this method const DerivIn &The derivative of x at t. time_typeThe value of the time, at which the step should be performed. StateOut &The result of the step is written in out. time_typeThe step size. This method performs one step. The derivative dxdt of in at the time t is passed to the method. The result is updated out-of-place, hence the input is in in and the output in out. Access to this step functionality is provided by explicit_error_stepper_base and do_step_impl should not be called directly. voidconst StateIn &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. const algebra_type &algebra_type()A copy of algebra is made and stored inside explicit_stepper_base. Constructs the runge_kutta_cash_karp54_classic class. This constructor can be used as a default constructor if the algebra has a default constructor. boolconst StateIn &

explicit_error_stepper_fsal_baseThe Runge-Kutta Dormand-Prince 5 method. The Runge-Kutta Dormand-Prince 5 method is a very popular method for solving ODEs, see . The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is available which make this method favourable for many applications.This class derives from explicit_error_stepper_fsal_base and inherits its interface via CRTP (current recurring template pattern). The method possesses the FSAL (first-same-as-last) property. See explicit_error_stepper_fsal_base for more details. explicit_error_stepper_fsal_base< runge_kutta_dopri5< ... >,... > stepper_base_type::state_type stepper_base_type::value_type stepper_base_type::deriv_type stepper_base_type::time_type stepper_base_type::algebra_type stepper_base_type::operations_type stepper_base_type::resizer_type voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. in is not modified in this method const DerivIn &The derivative of x at t. dxdt_in is not modified by this method time_typeThe value of the time, at which the step should be performed. StateOut &The result of the step is written in out. DerivOut &The result of the new derivative at time t+dt. time_typeThe step size. This method performs one step. The derivative dxdt_in of in at the time t is passed to the method. The result is updated out-of-place, hence the input is in in and the output in out. Furthermore, the derivative is update out-of-place, hence the input is assumed to be in dxdt_in and the output in dxdt_out. Access to this step functionality is provided by explicit_error_stepper_fsal_base and do_step_impl should not be called directly. voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. in is not modified in this method const DerivIn &The derivative of x at t. dxdt_in is not modified by this method time_typeThe value of the time, at which the step should be performed. StateOut &The result of the step is written in out. DerivOut &The result of the new derivative at time t+dt. time_typeThe step size. Err &An estimation of the error. This method performs one step. The derivative dxdt_in of in at the time t is passed to the method. The result is updated out-of-place, hence the input is in in and the output in out. Furthermore, the derivative is update out-of-place, hence the input is assumed to be in dxdt_in and the output in dxdt_out. Access to this step functionality is provided by explicit_error_stepper_fsal_base and do_step_impl should not be called directly. An estimation of the error is calculated. voidtime_typeStateOut &const StateIn1 &const DerivIn1 &time_typeconst StateIn2 &const DerivIn2 &time_typeThis method is used for continuous output and it calculates the state x at a time t from the knowledge of two states old_state and current_state at time points t_old and t_new. It also uses internal variables to calculate the result. Hence this method must be called after two successful do_step calls. voidconst StateIn &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. const algebra_type &algebra_type()A copy of algebra is made and stored inside explicit_stepper_base. Constructs the runge_kutta_dopri5 class. This constructor can be used as a default constructor if the algebra has a default constructor. boolconst StateIn & boolconst StateIn &

boost::numeric::odeint::explicit_error_generic_rk< StageCount, Order, StepperOrder, ErrorOrder, State, Value, Deriv, Time, Algebra, Operations, Resizer >The Runge-Kutta Fehlberg 78 method. The Runge-Kutta Fehlberg 78 method is a standard method for high-precision applications. The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is not available for this method.This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern). Furthermore, it derivs from explicit_error_generic_rk which is a generic Runge-Kutta algorithm with error estimation. For more details see explicit_error_stepper_base and explicit_error_generic_rk. stepper_base_type::state_type stepper_base_type::value_type stepper_base_type::deriv_type stepper_base_type::time_type stepper_base_type::algebra_type stepper_base_type::operations_type stepper_base_type::resizer_type voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. in is not modified in this method const DerivIn &The derivative of x at t. time_typeThe value of the time, at which the step should be performed. StateOut &The result of the step is written in out. time_typeThe step size. Err &The result of the error estimation is written in xerr. This method performs one step. The derivative dxdt of in at the time t is passed to the method. The result is updated out-of-place, hence the input is in in and the output in out. Futhermore, an estimation of the error is stored in xerr. do_step_impl is used by explicit_error_stepper_base. voidSystemThe system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. const StateIn &The state of the ODE which should be solved. in is not modified in this method const DerivIn &The derivative of x at t. time_typeThe value of the time, at which the step should be performed. StateOut &The result of the step is written in out. time_typeThe step size. This method performs one step. The derivative dxdt of in at the time t is passed to the method. The result is updated out-of-place, hence the input is in in and the output in out. Access to this step functionality is provided by explicit_stepper_base and do_step_impl should not be called directly. voidconst StateIn &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. const algebra_type &algebra_type()A copy of algebra is made and stored inside explicit_stepper_base. Constructs the runge_kutta_cash_fehlberg78 class. This constructor can be used as a default constructor if the algebra has a default constructor.

controlled_stepper_tagcontrolled_stepper_tag dense_output_stepper_tagdense_output_stepper_tag error_stepper_tagstepper_tag explicit_controlled_stepper_fsal_tagcontrolled_stepper_tag explicit_controlled_stepper_tagcontrolled_stepper_tag explicit_error_stepper_fsal_tagstepper_tag explicit_error_stepper_tagstepper_tag stepper_tagstepper_tag boost::numeric::odeint::stepper_tagboost::numeric::odeint::controlled_stepper_tagboost::numeric::odeint::controlled_stepper_tagboost::numeric::odeint::error_stepper_tagboost::numeric::odeint::error_stepper_tag

symplectic_nystroem_stepper_baseImplementation of the symplectic Euler method. The method is of first order and has one stage. It is described HERE. stepper_base_type::algebra_type stepper_base_type::value_type const algebra_type &algebra_type()A copy of algebra is made and stored inside explicit_stepper_base. Constructs the symplectic_euler. This constructor can be used as a default constructor if the algebra has a default constructor.

symplectic_nystroem_stepper_baseImplementation of the symmetric B3A Runge-Kutta Nystroem method of fifth order. The method is of fourth order and has five stages. It is described HERE. This method can be used with multiprecision types since the coefficients are defined analytically.ToDo: add reference to paper. stepper_base_type::algebra_type stepper_base_type::value_type const algebra_type &algebra_type()A copy of algebra is made and stored inside explicit_stepper_base. Constructs the symplectic_rkn_sb3a_m4_mclachlan. This constructor can be used as a default constructor if the algebra has a default constructor.

symplectic_nystroem_stepper_baseImplement of the symmetric B3A method of Runge-Kutta-Nystroem method of sixth order. The method is of fourth order and has six stages. It is described HERE. This method cannot be used with multiprecision types since the coefficients are not defined analytically.ToDo Add reference to the paper. stepper_base_type::algebra_type stepper_base_type::value_type const algebra_type &algebra_type()A copy of algebra is made and stored inside explicit_stepper_base. Constructs the symplectic_rkn_sb3a_mclachlan. This constructor can be used as a default constructor if the algebra has a default constructor.

algebra_stepper_base< Algebra, Operations >The Velocity-Verlet algorithm. The Velocity-Verlet algorithm is a method for simulation of molecular dynamics systems. It solves the ODE a=f(r,v',t) where r are the coordinates, v are the velocities and a are the accelerations, hence v = dr/dt, a=dv/dt. algebra_stepper_base< Algebra, Operations > algebra_stepper_base_type::algebra_type algebra_stepper_base_type::operations_type Coor Velocity Acceleration std::pair< coor_type, velocity_type > std::pair< velocity_type, acceleration_type > state_wrapper< acceleration_type > Value Time TimeSq Resizer stepper_tag unsigned short const order_type order_typevoid Returns the order of the stepper. voidSystemThe system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Second Order System concept. StateInOut &The state of the ODE which should be solved. The state is pair of Coor and Velocity. time_typeThe value of the time, at which the step should be performed. time_typeThe step size. This method performs one step. It transforms the result in-place. It can be used like pair< coordinates , velocities > state; stepper.do_step( sys , x , t , dt ); voidSystemThe system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Second Order System concept. const StateInOut &The state of the ODE which should be solved. The state is pair of Coor and Velocity. time_typeThe value of the time, at which the step should be performed. time_typeThe step size. This method performs one step. It transforms the result in-place. It can be used like pair< coordinates , velocities > state; stepper.do_step( sys , x , t , dt ); voidSystemThe system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Second Order System concept. CoorIn const &VelocityIn const &AccelerationIn const &CoorOut &VelocityOut &AccelerationOut &time_typeThe value of the time, at which the step should be performed. time_typeThe step size. This method performs one step. It transforms the result in-place. Additionally to the other methods the coordinates, velocities and accelerations are passed directly to do_step and they are transformed out-of-place. It can be used like coordinates qin , qout; velocities pin , pout; accelerations ain, aout; stepper.do_step( sys , qin , pin , ain , qout , pout , aout , t , dt ); voidconst StateIn &A state from which the size of the temporaries to be resized is deduced. Adjust the size of all temporaries in the stepper manually. voidvoidResets the internal state of this stepper. After calling this method it is safe to use all do_step method without explicitly initializing the stepper. voidconst AccelerationIn &Initializes the internal state of the stepper. voidSystemThe system function for the next calls of do_step. const CoorIn &The current coordinates of the ODE. const VelocityIn &The current velocities of the ODE. time_typeThe current time of the ODE. Initializes the internal state of the stepper. This method is equivalent to Acceleration a; system( qin , pin , a , t ); stepper.initialize( a ); boolvoid Returns if the stepper is initialized. const algebra_type &algebra_type()A copy of algebra is made and stored. Constructs the velocity_verlet class. This constructor can be used as a default constructor if the algebra has a default constructor. voidSystemconst CoorIn &const VelocityIn &time_type voidSystemStateInOut &time_typetime_type boolconst StateIn & acceleration_type &void const acceleration_type &void acceleration_type &void const acceleration_type &void voidvoid