| Brian Silverman | 7c33ab2 | 2018-08-04 17:14:51 -0700 | [diff] [blame^] | 1 | [/============================================================================ |
| 2 | Boost.odeint |
| 3 | |
| 4 | Copyright 2011-2012 Karsten Ahnert |
| 5 | Copyright 2011 Mario Mulansky |
| 6 | Copyright 2012 Sylwester Arabas |
| 7 | |
| 8 | Use, modification and distribution is subject to the Boost Software License, |
| 9 | Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at |
| 10 | http://www.boost.org/LICENSE_1_0.txt) |
| 11 | =============================================================================/] |
| 12 | |
| 13 | |
| 14 | [section Stepper] |
| 15 | |
| 16 | This concepts specifies the interface a simple stepper has to fulfill to be used within the __integrate_functions. |
| 17 | |
| 18 | [heading Description] |
| 19 | |
| 20 | The basic stepper concept. |
| 21 | A basic stepper following this Stepper concept is able to perform a single step of the solution /x(t)/ of an ODE to obtain /x(t+dt)/ using a given step size /dt/. |
| 22 | Basic steppers can be Runge-Kutta steppers, symplectic steppers as well as implicit steppers. |
| 23 | Depending on the actual stepper, the ODE is defined as __system, __symplectic_system, __simple_symplectic_system or __implicit_system. |
| 24 | Note that all error steppers are also basic steppers. |
| 25 | |
| 26 | [heading Refinement of] |
| 27 | |
| 28 | * DefaultConstructable |
| 29 | * CopyConstructable |
| 30 | |
| 31 | |
| 32 | [heading Associated types] |
| 33 | |
| 34 | * '''<para>'''[*state_type]'''</para>''' |
| 35 | '''<para>'''`Stepper::state_type`'''</para>''' |
| 36 | '''<para>'''The type characterizing the state of the ODE, hence ['x].'''</para>''' |
| 37 | |
| 38 | * '''<para>'''[*deriv_type]'''</para>''' |
| 39 | '''<para>'''`Stepper::deriv_type`'''</para>''' |
| 40 | '''<para>'''The type characterizing the derivative of the ODE, hence ['d x/dt].'''</para>''' |
| 41 | |
| 42 | * '''<para>'''[*time_type]'''</para>''' |
| 43 | '''<para>'''`Stepper::time_type`'''</para>''' |
| 44 | '''<para>'''The type characterizing the dependent variable of the ODE, hence the time ['t].'''</para>''' |
| 45 | |
| 46 | * '''<para>'''[*value_type]'''</para>''' |
| 47 | '''<para>'''`Stepper::value_type`'''</para>''' |
| 48 | '''<para>'''The numerical data type which is used within the stepper, something like `float`, `double`, `complex< double >`.'''</para>''' |
| 49 | |
| 50 | * '''<para>'''[*order_type]'''</para>''' |
| 51 | '''<para>'''`Stepper::order_type`'''</para>''' |
| 52 | '''<para>'''The type characterizing the order of the ODE, typically `unsigned short`.'''</para>''' |
| 53 | |
| 54 | * '''<para>'''[*stepper_category]'''</para>''' |
| 55 | '''<para>'''`Stepper::stepper_category`'''</para>''' |
| 56 | '''<para>'''A tag type characterizing the category of the stepper. This type must be convertible to `stepper_tag`.'''</para>''' |
| 57 | |
| 58 | |
| 59 | [heading Notation] |
| 60 | |
| 61 | [variablelist |
| 62 | [[`Stepper`] [A type that is a model of Stepper]] |
| 63 | [[`State`] [A type representing the state /x/ of the ODE]] |
| 64 | [[`Time`] [A type representing the time /t/ of the ODE]] |
| 65 | [[`stepper`] [An object of type `Stepper`]] |
| 66 | [[`x`] [Object of type `State`]] |
| 67 | [[`t`, `dt`] [Objects of type `Time`]] |
| 68 | [[`sys`] [An object defining the ODE. Depending on the Stepper this might be a model of __system, __symplectic_system, __simple_symplectic_system or __implicit_system ]] |
| 69 | ] |
| 70 | |
| 71 | [heading Valid Expressions] |
| 72 | |
| 73 | [table |
| 74 | [[Name] [Expression] [Type] [Semantics]] |
| 75 | [[Get the order] [`stepper.order()`] [`order_type`] [Returns the order of the stepper.]] |
| 76 | [[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 in `x`.] ] |
| 77 | |
| 78 | [/ [Do step with reference] [`stepper.do_step( boost::ref(sys) , x , t , dt )`] [`void`] [Performs one step of step size `dt`. The newly obtained state is written in place in `x`.] ] |
| 79 | |
| 80 | [/ [Do step out-of-place] [`stepper.do_step( sys , in , t , out , dt )`] [`void`] [Performs one step. The newly obtained state is written to `out`] ] |
| 81 | ] |
| 82 | |
| 83 | [heading Models] |
| 84 | |
| 85 | * `runge_kutta4` |
| 86 | * `euler` |
| 87 | * `runge_kutta_cash_karp54` |
| 88 | * `runge_kutta_dopri5` |
| 89 | * `runge_kutta_fehlberg78` |
| 90 | * `modified_midpoint` |
| 91 | * `rosenbrock4` |
| 92 | |
| 93 | [endsect] |