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74 lines
3.4 KiB
Plaintext
74 lines
3.4 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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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 Controlled Stepper]
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This concept specifies the interface a controlled stepper has to fulfill to be used within __integrate_functions.
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[heading Description]
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A 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/.
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Depending on an error estimate of the solution the step might be rejected and a smaller step-size is suggested.
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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>'''[*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 `controlled_stepper_tag`.'''</para>'''
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[heading Notation]
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[variablelist
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[[`ControlledStepper`] [A type that is a model of Controlled 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 `ControlledStepper`]]
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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, should 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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[[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.] ]
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[/ [Do step with reference] [`stepper.try_step( boost::ref(sys) , x , t , dt )`] [`void`] [Same as above with `System` as reference] ]
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]
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[heading Models]
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* `controlled_error_stepper< runge_kutta_cash_karp54 >`
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* `controlled_error_stepper_fsal< runge_kutta_dopri5 >`
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* `controlled_error_stepper< runge_kutta_fehlberg78 >`
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* `rosenbrock4_controller`
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* `bulirsch_stoer`
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[endsect]
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