| [/============================================================================ |
| 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] |
