| Brian Silverman | 7c33ab2 | 2018-08-04 17:14:51 -0700 | [diff] [blame^] | 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 | |
| 16 | This concept specifies the interface a dense output stepper has to fulfill to be used within __integrate_functions. |
| 17 | |
| 18 | [heading Description] |
| 19 | 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)/. |
| 20 | The step-size `dt` might be adjusted automatically due to error control. |
| 21 | Dense 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] |