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94 lines
3.7 KiB
Plaintext
94 lines
3.7 KiB
Plaintext
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[/============================================================================
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Boost.odeint
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Copyright 2011-2012 Karsten Ahnert
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Copyright 2011 Mario Mulansky
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Copyright 2012 Sylwester Arabas
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Use, modification and distribution is subject to the Boost Software License,
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Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt)
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=============================================================================/]
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[section Stepper]
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This concepts specifies the interface a simple stepper has to fulfill to be used within the __integrate_functions.
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[heading Description]
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The basic stepper concept.
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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/.
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Basic steppers can be Runge-Kutta steppers, symplectic steppers as well as implicit steppers.
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Depending on the actual stepper, the ODE is defined as __system, __symplectic_system, __simple_symplectic_system or __implicit_system.
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Note that all error steppers are also basic steppers.
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[heading Refinement of]
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* DefaultConstructable
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* CopyConstructable
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[heading Associated types]
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* '''<para>'''[*state_type]'''</para>'''
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'''<para>'''`Stepper::state_type`'''</para>'''
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'''<para>'''The type characterizing the state of the ODE, hence ['x].'''</para>'''
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* '''<para>'''[*deriv_type]'''</para>'''
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'''<para>'''`Stepper::deriv_type`'''</para>'''
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'''<para>'''The type characterizing the derivative of the ODE, hence ['d x/dt].'''</para>'''
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* '''<para>'''[*time_type]'''</para>'''
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'''<para>'''`Stepper::time_type`'''</para>'''
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'''<para>'''The type characterizing the dependent variable of the ODE, hence the time ['t].'''</para>'''
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* '''<para>'''[*value_type]'''</para>'''
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'''<para>'''`Stepper::value_type`'''</para>'''
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'''<para>'''The numerical data type which is used within the stepper, something like `float`, `double`, `complex< double >`.'''</para>'''
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* '''<para>'''[*order_type]'''</para>'''
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'''<para>'''`Stepper::order_type`'''</para>'''
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'''<para>'''The type characterizing the order of the ODE, typically `unsigned short`.'''</para>'''
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* '''<para>'''[*stepper_category]'''</para>'''
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'''<para>'''`Stepper::stepper_category`'''</para>'''
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'''<para>'''A tag type characterizing the category of the stepper. This type must be convertible to `stepper_tag`.'''</para>'''
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[heading Notation]
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[variablelist
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[[`Stepper`] [A type that is a model of Stepper]]
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[[`State`] [A type representing the state /x/ of the ODE]]
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[[`Time`] [A type representing the time /t/ of the ODE]]
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[[`stepper`] [An object of type `Stepper`]]
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[[`x`] [Object of type `State`]]
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[[`t`, `dt`] [Objects of type `Time`]]
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[[`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 ]]
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]
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[heading Valid Expressions]
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[table
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[[Name] [Expression] [Type] [Semantics]]
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[[Get the order] [`stepper.order()`] [`order_type`] [Returns the order of the stepper.]]
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[[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`.] ]
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[/ [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`.] ]
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[/ [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`] ]
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]
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[heading Models]
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* `runge_kutta4`
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* `euler`
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* `runge_kutta_cash_karp54`
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* `runge_kutta_dopri5`
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* `runge_kutta_fehlberg78`
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* `modified_midpoint`
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* `rosenbrock4`
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[endsect]
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