1[/============================================================================ 2 Boost.odeint 3 4 Copyright 2011-2012 Karsten Ahnert 5 Copyright 2011 Mario Mulansky 6 7 Use, modification and distribution is subject to the Boost Software License, 8 Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at 9 http://www.boost.org/LICENSE_1_0.txt) 10=============================================================================/] 11 12 13[section Controlled Stepper] 14 15This concept specifies the interface a controlled stepper has to fulfill to be used within __integrate_functions. 16 17[heading Description] 18 19A 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/. 20Depending on an error estimate of the solution the step might be rejected and a smaller step-size is suggested. 21 22[heading Associated types] 23 24* '''<para>'''[*state_type]'''</para>''' 25'''<para>'''`Stepper::state_type`'''</para>''' 26'''<para>'''The type characterizing the state of the ODE, hence ['x].'''</para>''' 27 28* '''<para>'''[*deriv_type]'''</para>''' 29'''<para>'''`Stepper::deriv_type`'''</para>''' 30'''<para>'''The type characterizing the derivative of the ODE, hence ['d x/dt].'''</para>''' 31 32* '''<para>'''[*time_type]'''</para>''' 33'''<para>'''`Stepper::time_type`'''</para>''' 34'''<para>'''The type characterizing the dependent variable of the ODE, hence the time ['t].'''</para>''' 35 36* '''<para>'''[*value_type]'''</para>''' 37'''<para>'''`Stepper::value_type`'''</para>''' 38'''<para>'''The numerical data type which is used within the stepper, something like `float`, `double`, `complex< double >`.'''</para>''' 39 40* '''<para>'''[*stepper_category]'''</para>''' 41'''<para>'''`Stepper::stepper_category`'''</para>''' 42'''<para>'''A tag type characterizing the category of the stepper. This type must be convertible to `controlled_stepper_tag`.'''</para>''' 43 44 45 46[heading Notation] 47 48[variablelist 49 [[`ControlledStepper`] [A type that is a model of Controlled Stepper]] 50 [[`State`] [A type representing the state /x/ of the ODE]] 51 [[`Time`] [A type representing the time /t/ of the ODE]] 52 [[`stepper`] [An object of type `ControlledStepper`]] 53 [[`x`] [Object of type `State`]] 54 [[`t`, `dt`] [Objects of type `Time`]] 55 [[`sys`] [An object defining the ODE, should be a model of __system, __symplectic_system, __simple_symplectic_system or __implicit_system.]] 56] 57 58[heading Valid Expressions] 59 60[table 61 [[Name] [Expression] [Type] [Semantics]] 62 [[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.] ] 63 [/ [Do step with reference] [`stepper.try_step( boost::ref(sys) , x , t , dt )`] [`void`] [Same as above with `System` as reference] ] 64] 65 66[heading Models] 67 68* `controlled_error_stepper< runge_kutta_cash_karp54 >` 69* `controlled_error_stepper_fsal< runge_kutta_dopri5 >` 70* `controlled_error_stepper< runge_kutta_fehlberg78 >` 71* `rosenbrock4_controller` 72* `bulirsch_stoer` 73 74[endsect]