1/*
2 [auto_generated]
3 boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp
4
5 [begin_description]
6 Implementation of the Runge Kutta Cash Karp 5(4) method. It uses the generic error stepper.
7 [end_description]
8
9 Copyright 2011-2013 Mario Mulansky
10 Copyright 2011-2013 Karsten Ahnert
11
12 Distributed under the Boost Software License, Version 1.0.
13 (See accompanying file LICENSE_1_0.txt or
14 copy at http://www.boost.org/LICENSE_1_0.txt)
15*/
16
17
18#ifndef BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_HPP_INCLUDED
19#define BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_HPP_INCLUDED
20
21#include <boost/fusion/container/vector.hpp>
22#include <boost/fusion/container/generation/make_vector.hpp>
23
24#include <boost/numeric/odeint/stepper/explicit_error_generic_rk.hpp>
25#include <boost/numeric/odeint/algebra/range_algebra.hpp>
26#include <boost/numeric/odeint/algebra/default_operations.hpp>
27#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
28#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
29
30#include <boost/numeric/odeint/util/state_wrapper.hpp>
31#include <boost/numeric/odeint/util/is_resizeable.hpp>
32#include <boost/numeric/odeint/util/resizer.hpp>
33
34#include <boost/array.hpp>
35
36
37
38
39namespace boost {
40namespace numeric {
41namespace odeint {
42
43
44#ifndef DOXYGEN_SKIP
45template< class Value = double >
46struct rk54_ck_coefficients_a1 : boost::array< Value , 1 >
47{
48 rk54_ck_coefficients_a1( void )
49 {
50 (*this)[0] = static_cast< Value >( 1 )/static_cast< Value >( 5 );
51 }
52};
53
54template< class Value = double >
55struct rk54_ck_coefficients_a2 : boost::array< Value , 2 >
56{
57 rk54_ck_coefficients_a2( void )
58 {
59 (*this)[0] = static_cast<Value>( 3 )/static_cast<Value>( 40 );
60 (*this)[1] = static_cast<Value>( 9 )/static_cast<Value>( 40 );
61 }
62};
63
64
65template< class Value = double >
66struct rk54_ck_coefficients_a3 : boost::array< Value , 3 >
67{
68 rk54_ck_coefficients_a3( void )
69 {
70 (*this)[0] = static_cast<Value>( 3 )/static_cast<Value>( 10 );
71 (*this)[1] = static_cast<Value>( -9 )/static_cast<Value>( 10 );
72 (*this)[2] = static_cast<Value>( 6 )/static_cast<Value>( 5 );
73 }
74};
75
76template< class Value = double >
77struct rk54_ck_coefficients_a4 : boost::array< Value , 4 >
78{
79 rk54_ck_coefficients_a4( void )
80 {
81 (*this)[0] = static_cast<Value>( -11 )/static_cast<Value>( 54 );
82 (*this)[1] = static_cast<Value>( 5 )/static_cast<Value>( 2 );
83 (*this)[2] = static_cast<Value>( -70 )/static_cast<Value>( 27 );
84 (*this)[3] = static_cast<Value>( 35 )/static_cast<Value>( 27 );
85 }
86};
87
88template< class Value = double >
89struct rk54_ck_coefficients_a5 : boost::array< Value , 5 >
90{
91 rk54_ck_coefficients_a5( void )
92 {
93 (*this)[0] = static_cast<Value>( 1631 )/static_cast<Value>( 55296 );
94 (*this)[1] = static_cast<Value>( 175 )/static_cast<Value>( 512 );
95 (*this)[2] = static_cast<Value>( 575 )/static_cast<Value>( 13824 );
96 (*this)[3] = static_cast<Value>( 44275 )/static_cast<Value>( 110592 );
97 (*this)[4] = static_cast<Value>( 253 )/static_cast<Value>( 4096 );
98 }
99};
100
101template< class Value = double >
102struct rk54_ck_coefficients_b : boost::array< Value , 6 >
103{
104 rk54_ck_coefficients_b( void )
105 {
106 (*this)[0] = static_cast<Value>( 37 )/static_cast<Value>( 378 );
107 (*this)[1] = static_cast<Value>( 0 );
108 (*this)[2] = static_cast<Value>( 250 )/static_cast<Value>( 621 );
109 (*this)[3] = static_cast<Value>( 125 )/static_cast<Value>( 594 );
110 (*this)[4] = static_cast<Value>( 0 );
111 (*this)[5] = static_cast<Value>( 512 )/static_cast<Value>( 1771 );
112 }
113};
114
115template< class Value = double >
116struct rk54_ck_coefficients_db : boost::array< Value , 6 >
117{
118 rk54_ck_coefficients_db( void )
119 {
120 (*this)[0] = static_cast<Value>( 37 )/static_cast<Value>( 378 ) - static_cast<Value>( 2825 )/static_cast<Value>( 27648 );
121 (*this)[1] = static_cast<Value>( 0 );
122 (*this)[2] = static_cast<Value>( 250 )/static_cast<Value>( 621 ) - static_cast<Value>( 18575 )/static_cast<Value>( 48384 );
123 (*this)[3] = static_cast<Value>( 125 )/static_cast<Value>( 594 ) - static_cast<Value>( 13525 )/static_cast<Value>( 55296 );
124 (*this)[4] = static_cast<Value>( -277 )/static_cast<Value>( 14336 );
125 (*this)[5] = static_cast<Value>( 512 )/static_cast<Value>( 1771 ) - static_cast<Value>( 1 )/static_cast<Value>( 4 );
126 }
127};
128
129
130template< class Value = double >
131struct rk54_ck_coefficients_c : boost::array< Value , 6 >
132{
133 rk54_ck_coefficients_c( void )
134 {
135 (*this)[0] = static_cast<Value>(0);
136 (*this)[1] = static_cast<Value>( 1 )/static_cast<Value>( 5 );
137 (*this)[2] = static_cast<Value>( 3 )/static_cast<Value>( 10 );
138 (*this)[3] = static_cast<Value>( 3 )/static_cast<Value>( 5 );
139 (*this)[4] = static_cast<Value>( 1 );
140 (*this)[5] = static_cast<Value>( 7 )/static_cast<Value>( 8 );
141 }
142};
143#endif
144
145
146template<
147 class State ,
148 class Value = double ,
149 class Deriv = State ,
150 class Time = Value ,
151 class Algebra = typename algebra_dispatcher< State >::algebra_type ,
152 class Operations = typename operations_dispatcher< State >::operations_type ,
153 class Resizer = initially_resizer
154 >
155#ifndef DOXYGEN_SKIP
156class runge_kutta_cash_karp54 : public explicit_error_generic_rk< 6 , 5 , 5 , 4 ,
157 State , Value , Deriv , Time , Algebra , Operations , Resizer >
158#else
159class runge_kutta_cash_karp54 : public explicit_error_generic_rk
160#endif
161{
162
163public:
164#ifndef DOXYGEN_SKIP
165 typedef explicit_error_generic_rk< 6 , 5 , 5 , 4 , State , Value , Deriv , Time ,
166 Algebra , Operations , Resizer > stepper_base_type;
167#endif
168 typedef typename stepper_base_type::state_type state_type;
169 typedef typename stepper_base_type::value_type value_type;
170 typedef typename stepper_base_type::deriv_type deriv_type;
171 typedef typename stepper_base_type::time_type time_type;
172 typedef typename stepper_base_type::algebra_type algebra_type;
173 typedef typename stepper_base_type::operations_type operations_type;
174 typedef typename stepper_base_type::resizer_type resizer_typ;
175
176 #ifndef DOXYGEN_SKIP
177 typedef typename stepper_base_type::stepper_type stepper_type;
178 typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
179 typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
180 #endif
181
182
183 runge_kutta_cash_karp54( const algebra_type &algebra = algebra_type() ) : stepper_base_type(
184 boost::fusion::make_vector( rk54_ck_coefficients_a1<Value>() ,
185 rk54_ck_coefficients_a2<Value>() ,
186 rk54_ck_coefficients_a3<Value>() ,
187 rk54_ck_coefficients_a4<Value>() ,
188 rk54_ck_coefficients_a5<Value>() ) ,
189 rk54_ck_coefficients_b<Value>() , rk54_ck_coefficients_db<Value>() , rk54_ck_coefficients_c<Value>() ,
190 algebra )
191 { }
192};
193
194
195/********** DOXYGEN **********/
196
197/**
198 * \class runge_kutta_cash_karp54
199 * \brief The Runge-Kutta Cash-Karp method.
200 *
201 * The Runge-Kutta Cash-Karp method is one of the standard methods for
202 * solving ordinary differential equations, see
203 * <a href="http://en.wikipedia.org/wiki/Cash%E2%80%93Karp_methods">en.wikipedia.org/wiki/Cash-Karp_methods</a>.
204 * The method is explicit and fulfills the Error Stepper concept. Step size control
205 * is provided but continuous output is not available for this method.
206 *
207 * This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern).
208 * Furthermore, it derivs from explicit_error_generic_rk which is a generic Runge-Kutta algorithm with error estimation.
209 * For more details see explicit_error_stepper_base and explicit_error_generic_rk.
210 *
211 * \tparam State The state type.
212 * \tparam Value The value type.
213 * \tparam Deriv The type representing the time derivative of the state.
214 * \tparam Time The time representing the independent variable - the time.
215 * \tparam Algebra The algebra type.
216 * \tparam Operations The operations type.
217 * \tparam Resizer The resizer policy type.
218 */
219
220
221 /**
222 * \fn runge_kutta_cash_karp54::runge_kutta_cash_karp54( const algebra_type &algebra )
223 * \brief Constructs the runge_kutta_cash_karp54 class. This constructor can be used as a default
224 * constructor if the algebra has a default constructor.
225 * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
226 */
227}
228}
229}
230
231#endif // BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_HPP_INCLUDED
232

source code of boost/boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp