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