EQ2EMu/EQ2/source/depends/boost_1_72_0/libs/numeric/odeint/doc/concepts/controlled_stepper.qbk

[/============================================================================
  Boost.odeint

  Copyright 2011-2012 Karsten Ahnert
  Copyright 2011 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 Controlled Stepper]

This concept specifies the interface a controlled stepper has to fulfill to be used within __integrate_functions.

[heading Description]

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/.
Depending on an error estimate of the solution the step might be rejected and a smaller step-size is suggested.

[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&lt; double &gt;`.'''</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 `controlled_stepper_tag`.'''</para>'''



[heading Notation]

[variablelist 
  [[`ControlledStepper`] [A type that is a model of Controlled Stepper]]
  [[`State`] [A type representing the state /x/ of the ODE]]
  [[`Time`] [A type representing the time /t/ of the ODE]]
  [[`stepper`] [An object of type `ControlledStepper`]]
  [[`x`] [Object of type `State`]]
  [[`t`, `dt`] [Objects of type `Time`]]
  [[`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]]
  [[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.] ]
  [/ [Do step with reference] [`stepper.try_step( boost::ref(sys) , x , t , dt )`] [`void`] [Same as above with `System` as reference] ]
]

[heading Models]

* `controlled_error_stepper< runge_kutta_cash_karp54 >`
* `controlled_error_stepper_fsal< runge_kutta_dopri5 >`
* `controlled_error_stepper< runge_kutta_fehlberg78 >`
* `rosenbrock4_controller`
* `bulirsch_stoer`

[endsect]