| [/============================================================================ |
| Boost.odeint |
| |
| Copyright 2011-2013 Karsten Ahnert |
| Copyright 2011 Mario Mulansky |
| Copyright 2012 Sylwester Arabas |
| |
| 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 Error Stepper] |
| |
| This concepts specifies the interface an error stepper has to fulfill to be used within a ControlledErrorStepper. An error stepper must always fulfill the stepper concept. This can trivially implemented by |
| |
| `` |
| template< class System > |
| error_stepper::do_step( System sys , state_type &x , time_type t , time_type dt ) |
| { |
| state_type xerr; |
| // allocate xerr |
| do_step( sys , x , t , dt , xerr ); |
| } |
| `` |
| |
| [heading Description] |
| |
| An error stepper following this Error Stepper concept is capable of doing one step of the solution /x(t)/ of an ODE with step-size /dt/ to obtain /x(t+dt)/ and also computing an error estimate ['x[sub err]] of the result. |
| Error Steppers can be Runge-Kutta steppers, symplectic steppers as well as implicit steppers. |
| Based on the stepper type, the ODE is defined as __system, __symplectic_system, __simple_symplectic_system or __implicit_system. |
| |
| [heading Refinement of] |
| |
| * DefaultConstructable |
| * CopyConstructable |
| * Stepper |
| |
| [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>'''[*order_type]'''</para>''' |
| '''<para>'''`Stepper::order_type`'''</para>''' |
| '''<para>'''The type characterizing the order of the ODE, typically `unsigned short`.'''</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 `error_stepper_tag`.'''</para>''' |
| |
| |
| [heading Notation] |
| |
| [variablelist |
| [[`ErrorStepper`] [A type that is a model of Error Stepper]] |
| [[`State`] [A type representing the state /x/ of the ODE]] |
| [[`Error`] [A type representing the error calculated by the stepper, usually same as `State`]] |
| [[`Time`] [A type representing the time /t/ of the ODE]] |
| [[`stepper`] [An object of type `ErrorStepper`]] |
| [[`x`] [Object of type `State`]] |
| [[`xerr`] [Object of type `Error`]] |
| [[`t`, `dt`] [Objects of type `Time`]] |
| [[`sys`] [An object defining the ODE, should be a model of either __system, __symplectic_system, __simple_symplectic_system or __implicit_system.]] |
| ] |
| |
| [heading Valid Expressions] |
| |
| [table |
| [[Name] [Expression] [Type] [Semantics]] |
| [[Get the stepper order] [`stepper.order()`] [`order_type`] [Returns the order of the stepper for one step without error estimation.]] |
| [[Get the stepper order] [`stepper.stepper_order()`] [`order_type`] [Returns the order of the stepper for one error estimation step which is used for error calculation.]] |
| [[Get the error order] [`stepper.errorr_order()`] [`order_type`] [Returns the order of the error step which is used for error calculation.]] |
| [[Do step] [`stepper.do_step( sys , x , t , dt )`] [`void`] [Performs one step of step size `dt`. The newly obtained state is written in-place to `x`.] ] |
| [[Do step with error estimation] [`stepper.do_step( sys , x , t , dt , xerr )`] [`void`] [Performs one step of step size `dt` with error estimation. The newly obtained state is written in-place to `x` and the estimated error to `xerr`.] ] |
| [/ [Do step with reference] [`stepper.do_step( boost::ref(sys) , x , t , dt , xerr )`] [`void`] [Performs one step of step size `dt`. The newly obtained state is written in-place to `x` and the estimated error to `xerr`.] ] |
| ] |
| |
| [heading Models] |
| |
| * `runge_kutta_cash_karp54` |
| * `runge_kutta_dopri5` |
| * `runge_kutta_fehlberg78` |
| * `rosenbrock4` |
| |
| [endsect] |