| 12345678910111213141516171819202122232425262728293031323334353637383940414243 |
- [/============================================================================
- Boost.odeint
- Copyright 2011 Mario Mulansky
- Copyright 2011-2012 Karsten Ahnert
- 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 Implicit System]
- [heading Description]
- This concept describes how to define a ODE that can be solved by an implicit routine.
- Implicit routines need not only the function /f(x,t)/ but also the Jacobian /df/dx = A(x,t)/.
- /A/ is a matrix and implicit routines need to solve the linear problem /Ax = b/.
- In odeint this is implemented with use of __ublas, therefore, the ['state_type] implicit routines is ['ublas::vector] and the matrix is defined as ['ublas::matrix].
- [heading Notation]
- [variablelist
- [[`System`] [A type that is a model of `Implicit System`]]
- [[`Time`] [A type representing the time of the ODE]]
- [[`sys`] [An object of type `System`]]
- [[`x`] [Object of type ublas::vector]]
- [[`dxdt`] [Object of type ublas::vector]]
- [[`jacobi`] [Object of type ublas::matrix]]
- [[`t`] [Object of type `Time`]]
- ]
- [heading Valid Expressions]
- [table
- [[Name] [Expression] [Type] [Semantics]]
- [[Calculate ['dx/dt := f(x,t)]] [`sys.first( x , dxdt , t )`] [`void`] [Calculates `f(x,t)`, the result is stored into dxdt] ]
- [[Calculate ['A := df/dx (x,t)]] [`sys.second( x , jacobi , t )`] [`void`] [Calculates the Jacobian of /f/ at /x/,/t/, the result is stored into `jacobi`] ]
- ]
- [endsect]
|
