1[/============================================================================ 2 Boost.odeint 3 4 Copyright (c) 2009-2013 Karsten Ahnert 5 Copyright (c) 2009-2013 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 14[section Dense Output Stepper] 15 16This concept specifies the interface a dense output stepper has to fulfill to be used within __integrate_functions. 17 18[heading Description] 19A 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)/. 20The step-size `dt` might be adjusted automatically due to error control. 21Dense output steppers also can interpolate the solution to calculate the state /x(t')/ at any point /t <= t' <= t+dt/. 22 23[heading Associated types] 24 25* '''<para>'''[*state_type]'''</para>''' 26'''<para>'''`Stepper::state_type`'''</para>''' 27'''<para>'''The type characterizing the state of the ODE, hence ['x].'''</para>''' 28 29* '''<para>'''[*deriv_type]'''</para>''' 30'''<para>'''`Stepper::deriv_type`'''</para>''' 31'''<para>'''The type characterizing the derivative of the ODE, hence ['d x/dt].'''</para>''' 32 33* '''<para>'''[*time_type]'''</para>''' 34'''<para>'''`Stepper::time_type`'''</para>''' 35'''<para>'''The type characterizing the dependent variable of the ODE, hence the time ['t].'''</para>''' 36 37* '''<para>'''[*value_type]'''</para>''' 38'''<para>'''`Stepper::value_type`'''</para>''' 39'''<para>'''The numerical data type which is used within the stepper, something like `float`, `double`, `complex< double >`.'''</para>''' 40 41* '''<para>'''[*stepper_category]'''</para>''' 42'''<para>'''`Stepper::stepper_category`'''</para>''' 43'''<para>'''A tag type characterizing the category of the stepper. This type must be convertible to `dense_output_stepper_tag`.'''</para>''' 44 45 46[heading Notation] 47 48[variablelist 49 [[`Stepper`] [A type that is a model of Dense Output Stepper]] 50 [[`State`] [A type representing the state /x/ of the ODE]] 51 [[`stepper`] [An object of type `Stepper`]] 52 [[`x0`, `x`] [Object of type `State`]] 53 [[`t0`, `dt0`, `t`] [Objects of type `Stepper::time_type`]] 54 [[`sys`] [An object defining the ODE, should be a model of __system, __symplectic_system, __simple_symplectic_system or __implicit_system.]] 55] 56 57[heading Valid Expressions] 58 59[table 60 [[Name] [Expression] [Type] [Semantics]] 61 62 [[Initialize integration] [`stepper.initialize( x0 , t0 , dt0 )`] [void] [Initializes the stepper with initial values `x0`, `t0` and `dt0`.]] 63 64 [[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.] ] 65 66 [/ [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] ] 67 68 [[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/.]] 69 70 [[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`]] 71 72 [[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()`]] 73 74 [[Get current time step] [`stepper.current_time_step()`] [`const 75 Stepper::time_type&`] [Returns the current step size of the stepper, that is 76 /dt/]] 77] 78 79[heading Models] 80 81* `dense_output_controlled_explicit_fsal< controlled_error_stepper_fsal< runge_kutta_dopri5 >` 82* `bulirsch_stoer_dense_out` 83* `rosenbrock4_dense_output` 84 85[endsect] 86