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102 lines
4.5 KiB
Plaintext
102 lines
4.5 KiB
Plaintext
[/============================================================================
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Boost.odeint
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Copyright 2011-2013 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 Error Stepper]
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This concepts specifies the interface an error stepper has to fulfill to be used within a ControlledErrorStepper. An error stepper must always fulfill the stepper concept. This can trivially implemented by
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``
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template< class System >
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error_stepper::do_step( System sys , state_type &x , time_type t , time_type dt )
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{
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state_type xerr;
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// allocate xerr
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do_step( sys , x , t , dt , xerr );
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}
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``
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[heading Description]
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An error stepper following this Error Stepper concept is capable of doing one step of the solution /x(t)/ of an ODE with step-size /dt/ to obtain /x(t+dt)/ and also computing an error estimate ['x[sub err]] of the result.
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Error Steppers can be Runge-Kutta steppers, symplectic steppers as well as implicit steppers.
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Based on the stepper type, the ODE is defined as __system, __symplectic_system, __simple_symplectic_system or __implicit_system.
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[heading Refinement of]
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* DefaultConstructable
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* CopyConstructable
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* Stepper
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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 `error_stepper_tag`.'''</para>'''
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[heading Notation]
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[variablelist
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[[`ErrorStepper`] [A type that is a model of Error Stepper]]
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[[`State`] [A type representing the state /x/ of the ODE]]
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[[`Error`] [A type representing the error calculated by the stepper, usually same as `State`]]
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[[`Time`] [A type representing the time /t/ of the ODE]]
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[[`stepper`] [An object of type `ErrorStepper`]]
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[[`x`] [Object of type `State`]]
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[[`xerr`] [Object of type `Error`]]
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[[`t`, `dt`] [Objects of type `Time`]]
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[[`sys`] [An object defining the ODE, should be a model of either __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 stepper order] [`stepper.order()`] [`order_type`] [Returns the order of the stepper for one step without error estimation.]]
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[[Get the stepper order] [`stepper.stepper_order()`] [`order_type`] [Returns the order of the stepper for one error estimation step which is used for error calculation.]]
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[[Get the error order] [`stepper.errorr_order()`] [`order_type`] [Returns the order of the error step which is used for error calculation.]]
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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 to `x`.] ]
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[[Do step with error estimation] [`stepper.do_step( sys , x , t , dt , xerr )`] [`void`] [Performs one step of step size `dt` with error estimation. The newly obtained state is written in-place to `x` and the estimated error to `xerr`.] ]
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[/ [Do step with reference] [`stepper.do_step( boost::ref(sys) , x , t , dt , xerr )`] [`void`] [Performs one step of step size `dt`. The newly obtained state is written in-place to `x` and the estimated error to `xerr`.] ]
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]
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[heading Models]
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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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* `rosenbrock4`
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[endsect]
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