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- [/============================================================================
- Boost.odeint
- Copyright 2011-2012 Karsten Ahnert
- Copyright 2011 Mario Mulansky
- Use, modification and distribution is subject to the Boost Software License,
- Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
- http://www.boost.org/LICENSE_1_0.txt)
- =============================================================================/]
- [section Controlled Stepper]
- This concept specifies the interface a controlled stepper has to fulfill to be used within __integrate_functions.
- [heading Description]
- A controlled stepper following this Controlled Stepper concept provides the possibility to perform one step of the solution /x(t)/ of an ODE with step-size /dt/ to obtain /x(t+dt)/ with a given step-size /dt/.
- Depending on an error estimate of the solution the step might be rejected and a smaller step-size is suggested.
- [heading Associated types]
- * '''<para>'''[*state_type]'''</para>'''
- '''<para>'''`Stepper::state_type`'''</para>'''
- '''<para>'''The type characterizing the state of the ODE, hence ['x].'''</para>'''
- * '''<para>'''[*deriv_type]'''</para>'''
- '''<para>'''`Stepper::deriv_type`'''</para>'''
- '''<para>'''The type characterizing the derivative of the ODE, hence ['d x/dt].'''</para>'''
- * '''<para>'''[*time_type]'''</para>'''
- '''<para>'''`Stepper::time_type`'''</para>'''
- '''<para>'''The type characterizing the dependent variable of the ODE, hence the time ['t].'''</para>'''
- * '''<para>'''[*value_type]'''</para>'''
- '''<para>'''`Stepper::value_type`'''</para>'''
- '''<para>'''The numerical data type which is used within the stepper, something like `float`, `double`, `complex< double >`.'''</para>'''
- * '''<para>'''[*stepper_category]'''</para>'''
- '''<para>'''`Stepper::stepper_category`'''</para>'''
- '''<para>'''A tag type characterizing the category of the stepper. This type must be convertible to `controlled_stepper_tag`.'''</para>'''
- [heading Notation]
- [variablelist
- [[`ControlledStepper`] [A type that is a model of Controlled Stepper]]
- [[`State`] [A type representing the state /x/ of the ODE]]
- [[`Time`] [A type representing the time /t/ of the ODE]]
- [[`stepper`] [An object of type `ControlledStepper`]]
- [[`x`] [Object of type `State`]]
- [[`t`, `dt`] [Objects of type `Time`]]
- [[`sys`] [An object defining the ODE, should be a model of __system, __symplectic_system, __simple_symplectic_system or __implicit_system.]]
- ]
- [heading Valid Expressions]
- [table
- [[Name] [Expression] [Type] [Semantics]]
- [[Do step] [``stepper.try_step( sys , x , t , dt )``] [`controlled_step_result`] [Tries one step of step size `dt`. If the step was successful, `success` is returned, the resulting state is written to `x`, the new time is stored in `t` and `dt` now contains a new (possibly larger) step-size for the next step. If the error was too big, `rejected` is returned and the results are neglected - `x` and `t` are unchanged and `dt` now contains a reduced step-size to be used for the next try.] ]
- [/ [Do step with reference] [`stepper.try_step( boost::ref(sys) , x , t , dt )`] [`void`] [Same as above with `System` as reference] ]
- ]
- [heading Models]
- * `controlled_error_stepper< runge_kutta_cash_karp54 >`
- * `controlled_error_stepper_fsal< runge_kutta_dopri5 >`
- * `controlled_error_stepper< runge_kutta_fehlberg78 >`
- * `rosenbrock4_controller`
- * `bulirsch_stoer`
- [endsect]
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