1[/============================================================================ 2 Boost.odeint 3 4 Copyright 2011-2012 Karsten Ahnert 5 Copyright 2011 Mario Mulansky 6 Copyright 2012 Sylwester Arabas 7 8 Use, modification and distribution is subject to the Boost Software License, 9 Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at 10 http://www.boost.org/LICENSE_1_0.txt) 11=============================================================================/] 12 13 14[section Stepper] 15 16This concepts specifies the interface a simple stepper has to fulfill to be used within the __integrate_functions. 17 18[heading Description] 19 20The basic stepper concept. 21A basic stepper following this Stepper concept is able to perform a single step of the solution /x(t)/ of an ODE to obtain /x(t+dt)/ using a given step size /dt/. 22Basic steppers can be Runge-Kutta steppers, symplectic steppers as well as implicit steppers. 23Depending on the actual stepper, the ODE is defined as __system, __symplectic_system, __simple_symplectic_system or __implicit_system. 24Note that all error steppers are also basic steppers. 25 26[heading Refinement of] 27 28* DefaultConstructable 29* CopyConstructable 30 31 32[heading Associated types] 33 34* '''<para>'''[*state_type]'''</para>''' 35'''<para>'''`Stepper::state_type`'''</para>''' 36'''<para>'''The type characterizing the state of the ODE, hence ['x].'''</para>''' 37 38* '''<para>'''[*deriv_type]'''</para>''' 39'''<para>'''`Stepper::deriv_type`'''</para>''' 40'''<para>'''The type characterizing the derivative of the ODE, hence ['d x/dt].'''</para>''' 41 42* '''<para>'''[*time_type]'''</para>''' 43'''<para>'''`Stepper::time_type`'''</para>''' 44'''<para>'''The type characterizing the dependent variable of the ODE, hence the time ['t].'''</para>''' 45 46* '''<para>'''[*value_type]'''</para>''' 47'''<para>'''`Stepper::value_type`'''</para>''' 48'''<para>'''The numerical data type which is used within the stepper, something like `float`, `double`, `complex< double >`.'''</para>''' 49 50* '''<para>'''[*order_type]'''</para>''' 51'''<para>'''`Stepper::order_type`'''</para>''' 52'''<para>'''The type characterizing the order of the ODE, typically `unsigned short`.'''</para>''' 53 54* '''<para>'''[*stepper_category]'''</para>''' 55'''<para>'''`Stepper::stepper_category`'''</para>''' 56'''<para>'''A tag type characterizing the category of the stepper. This type must be convertible to `stepper_tag`.'''</para>''' 57 58 59[heading Notation] 60 61[variablelist 62 [[`Stepper`] [A type that is a model of Stepper]] 63 [[`State`] [A type representing the state /x/ of the ODE]] 64 [[`Time`] [A type representing the time /t/ of the ODE]] 65 [[`stepper`] [An object of type `Stepper`]] 66 [[`x`] [Object of type `State`]] 67 [[`t`, `dt`] [Objects of type `Time`]] 68 [[`sys`] [An object defining the ODE. Depending on the Stepper this might be a model of __system, __symplectic_system, __simple_symplectic_system or __implicit_system ]] 69] 70 71[heading Valid Expressions] 72 73[table 74 [[Name] [Expression] [Type] [Semantics]] 75 [[Get the order] [`stepper.order()`] [`order_type`] [Returns the order of the stepper.]] 76 [[Do step] [`stepper.do_step( sys , x , t , dt )`] [`void`] [Performs one step of step size `dt`. The newly obtained state is written in place in `x`.] ] 77 78 [/ [Do step with reference] [`stepper.do_step( boost::ref(sys) , x , t , dt )`] [`void`] [Performs one step of step size `dt`. The newly obtained state is written in place in `x`.] ] 79 80 [/ [Do step out-of-place] [`stepper.do_step( sys , in , t , out , dt )`] [`void`] [Performs one step. The newly obtained state is written to `out`] ] 81] 82 83[heading Models] 84 85* `runge_kutta4` 86* `euler` 87* `runge_kutta_cash_karp54` 88* `runge_kutta_dopri5` 89* `runge_kutta_fehlberg78` 90* `modified_midpoint` 91* `rosenbrock4` 92 93[endsect] 94