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