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- [/============================================================================
- Boost.odeint
- Copyright (c) 2009-2013 Karsten Ahnert
- Copyright (c) 2009-2013 Mario Mulansky
- 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 Dense Output Stepper]
- This concept specifies the interface a dense output stepper has to fulfill to be used within __integrate_functions.
- [heading Description]
- 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)/.
- The step-size `dt` might be adjusted automatically due to error control.
- Dense output steppers also can interpolate the solution to calculate the state /x(t')/ at any point /t <= t' <= t+dt/.
- [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>'''[*stepper_category]'''</para>'''
- '''<para>'''`Stepper::stepper_category`'''</para>'''
- '''<para>'''A tag type characterizing the category of the stepper. This type must be convertible to `dense_output_stepper_tag`.'''</para>'''
- [heading Notation]
- [variablelist
- [[`Stepper`] [A type that is a model of Dense Output Stepper]]
- [[`State`] [A type representing the state /x/ of the ODE]]
- [[`stepper`] [An object of type `Stepper`]]
- [[`x0`, `x`] [Object of type `State`]]
- [[`t0`, `dt0`, `t`] [Objects of type `Stepper::time_type`]]
- [[`sys`] [An object defining the ODE, should be a model of __system, __symplectic_system, __simple_symplectic_system or __implicit_system.]]
- ]
- [heading Valid Expressions]
- [table
- [[Name] [Expression] [Type] [Semantics]]
- [[Initialize integration] [`stepper.initialize( x0 , t0 , dt0 )`] [void] [Initializes the stepper with initial values `x0`, `t0` and `dt0`.]]
- [[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.] ]
- [/ [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] ]
- [[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/.]]
- [[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`]]
- [[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()`]]
- [[Get current time step] [`stepper.current_time_step()`] [`const
- Stepper::time_type&`] [Returns the current step size of the stepper, that is
- /dt/]]
- ]
- [heading Models]
- * `dense_output_controlled_explicit_fsal< controlled_error_stepper_fsal< runge_kutta_dopri5 >`
- * `bulirsch_stoer_dense_out`
- * `rosenbrock4_dense_output`
- [endsect]
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