| [/============================================================================ |
| Boost.odeint |
| |
| Copyright 2011-2012 Karsten Ahnert |
| Copyright 2011 Mario Mulansky |
| Copyright 2012 Sylwester Arabas |
| |
| 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 Stepper] |
| |
| This concepts specifies the interface a simple stepper has to fulfill to be used within the __integrate_functions. |
| |
| [heading Description] |
| |
| The basic stepper concept. |
| A 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/. |
| Basic steppers can be Runge-Kutta steppers, symplectic steppers as well as implicit steppers. |
| Depending on the actual stepper, the ODE is defined as __system, __symplectic_system, __simple_symplectic_system or __implicit_system. |
| Note that all error steppers are also basic steppers. |
| |
| [heading Refinement of] |
| |
| * DefaultConstructable |
| * CopyConstructable |
| |
| |
| [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>'''[*order_type]'''</para>''' |
| '''<para>'''`Stepper::order_type`'''</para>''' |
| '''<para>'''The type characterizing the order of the ODE, typically `unsigned short`.'''</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 `stepper_tag`.'''</para>''' |
| |
| |
| [heading Notation] |
| |
| [variablelist |
| [[`Stepper`] [A type that is a model of 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 `Stepper`]] |
| [[`x`] [Object of type `State`]] |
| [[`t`, `dt`] [Objects of type `Time`]] |
| [[`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 ]] |
| ] |
| |
| [heading Valid Expressions] |
| |
| [table |
| [[Name] [Expression] [Type] [Semantics]] |
| [[Get the order] [`stepper.order()`] [`order_type`] [Returns the order of the stepper.]] |
| [[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`.] ] |
| |
| [/ [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`.] ] |
| |
| [/ [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`] ] |
| ] |
| |
| [heading Models] |
| |
| * `runge_kutta4` |
| * `euler` |
| * `runge_kutta_cash_karp54` |
| * `runge_kutta_dopri5` |
| * `runge_kutta_fehlberg78` |
| * `modified_midpoint` |
| * `rosenbrock4` |
| |
| [endsect] |