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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] |