ceph/src/boost/libs/numeric/odeint/doc/concepts/controlled_stepper.qbk

   1 [/============================================================================
   2   Boost.odeint
   3
   4   Copyright 2011-2012 Karsten Ahnert
   5   Copyright 2011 Mario Mulansky
   6
   7   Use, modification and distribution is subject to the Boost Software License,
   8   Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
   9   http://www.boost.org/LICENSE_1_0.txt)
  10 =============================================================================/]
  11
  12
  13 [section Controlled Stepper]
  14
  15 This concept specifies the interface a controlled stepper has to fulfill to be used within __integrate_functions.
  16
  17 [heading Description]
  18
  19 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/.
  20 Depending on an error estimate of the solution the step might be rejected and a smaller step-size is suggested.
  21
  22 [heading Associated types]
  23
  24 *  '''<para>'''[*state_type]'''</para>'''
  25 '''<para>'''`Stepper::state_type`'''</para>'''
  26 '''<para>'''The type characterizing the state of the ODE, hence ['x].'''</para>'''
  27
  28 *  '''<para>'''[*deriv_type]'''</para>'''
  29 '''<para>'''`Stepper::deriv_type`'''</para>'''
  30 '''<para>'''The type characterizing the derivative of the ODE, hence ['d x/dt].'''</para>'''
  31
  32 *  '''<para>'''[*time_type]'''</para>'''
  33 '''<para>'''`Stepper::time_type`'''</para>'''
  34 '''<para>'''The type characterizing the dependent variable of the ODE, hence the time ['t].'''</para>'''
  35
  36 *  '''<para>'''[*value_type]'''</para>'''
  37 '''<para>'''`Stepper::value_type`'''</para>'''
  38 '''<para>'''The numerical data type which is used within the stepper, something like `float`, `double`, `complex&lt; double &gt;`.'''</para>'''
  39
  40 *  '''<para>'''[*stepper_category]'''</para>'''
  41 '''<para>'''`Stepper::stepper_category`'''</para>'''
  42 '''<para>'''A tag type characterizing the category of the stepper. This type must be convertible to `controlled_stepper_tag`.'''</para>'''
  43
  44
  45
  46 [heading Notation]
  47
  48 [variablelist
  49   [[`ControlledStepper`] [A type that is a model of Controlled Stepper]]
  50   [[`State`] [A type representing the state /x/ of the ODE]]
  51   [[`Time`] [A type representing the time /t/ of the ODE]]
  52   [[`stepper`] [An object of type `ControlledStepper`]]
  53   [[`x`] [Object of type `State`]]
  54   [[`t`, `dt`] [Objects of type `Time`]]
  55   [[`sys`] [An object defining the ODE, should be a model of __system, __symplectic_system, __simple_symplectic_system or __implicit_system.]]
  56 ]
  57
  58 [heading Valid Expressions]
  59
  60 [table
  61   [[Name] [Expression] [Type] [Semantics]]
  62   [[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.] ]
  63   [/ [Do step with reference] [`stepper.try_step( boost::ref(sys) , x , t , dt )`] [`void`] [Same as above with `System` as reference] ]
  64 ]
  65
  66 [heading Models]
  67
  68 * `controlled_error_stepper< runge_kutta_cash_karp54 >`
  69 * `controlled_error_stepper_fsal< runge_kutta_dopri5 >`
  70 * `controlled_error_stepper< runge_kutta_fehlberg78 >`
  71 * `rosenbrock4_controller`
  72 * `bulirsch_stoer`
  73
  74 [endsect]