86 lines
4.1 KiB
Plaintext
86 lines
4.1 KiB
Plaintext
[/============================================================================
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Boost.odeint
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Copyright (c) 2009-2013 Karsten Ahnert
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Copyright (c) 2009-2013 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 Dense Output Stepper]
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This concept specifies the interface a dense output stepper has to fulfill to be used within __integrate_functions.
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[heading Description]
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A dense output stepper following this Dense Output Stepper concept provides the possibility to perform a single step of the solution /x(t)/ of an ODE to obtain /x(t+dt)/.
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The step-size `dt` might be adjusted automatically due to error control.
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Dense output steppers also can interpolate the solution to calculate the state /x(t')/ at any point /t <= t' <= t+dt/.
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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 `dense_output_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 Dense Output Stepper]]
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[[`State`] [A type representing the state /x/ of the ODE]]
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[[`stepper`] [An object of type `Stepper`]]
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[[`x0`, `x`] [Object of type `State`]]
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[[`t0`, `dt0`, `t`] [Objects of type `Stepper::time_type`]]
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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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[[Initialize integration] [`stepper.initialize( x0 , t0 , dt0 )`] [void] [Initializes the stepper with initial values `x0`, `t0` and `dt0`.]]
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[[Do step] [`stepper.do_step( sys )`] [`std::pair< Stepper::time_type , Stepper::time_type >`] [Performs one step using the ODE defined by `sys`. The step-size might be changed internally due to error control. This function returns a pair containing `t` and `t+dt` representing the interval for which interpolation can be performed.] ]
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[/ [Do step with reference] [`stepper.do_step( boost::ref( sys ) )`] [`std::pair< Stepper::time_type , Stepper::time_type >`] [Same as above with `System` as reference] ]
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[[Do interpolation] [`stepper.calc_state( t_inter , x )`] [`void`] [Performs the interpolation to calculate /x(t[sub inter]/) where /t <= t[sub inter] <= t+dt/.]]
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[[Get current time] [`stepper.current_time()`] [`const Stepper::time_type&`] [Returns the current time /t+dt/ of the stepper, that is the end time of the last step and the starting time for the next call of `do_step`]]
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[[Get current state] [`stepper.current_state()`] [`const Stepper::state_type&`] [Returns the current state of the stepper, that is /x(t+dt)/, the state at the time returned by `stepper.current_time()`]]
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[[Get current time step] [`stepper.current_time_step()`] [`const
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Stepper::time_type&`] [Returns the current step size of the stepper, that is
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/dt/]]
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]
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[heading Models]
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* `dense_output_controlled_explicit_fsal< controlled_error_stepper_fsal< runge_kutta_dopri5 >`
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* `bulirsch_stoer_dense_out`
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* `rosenbrock4_dense_output`
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[endsect]
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