46 template< class Value = double >
47 struct rk78_coefficients_a1 : boost::array< Value , 1 >
51         (*this)[0] = static_cast< Value >( 2 )/static_cast< Value >( 27 );  in rk78_coefficients_a1()
55 template< class Value = double >
56 struct rk78_coefficients_a2 : boost::array< Value , 2 >
60         (*this)[0] = static_cast< Value >( 1 )/static_cast< Value >( 36 );  in rk78_coefficients_a2()
61         (*this)[1] = static_cast< Value >( 1 )/static_cast< Value >( 12 );  in rk78_coefficients_a2()
66 template< class Value = double >
67 struct rk78_coefficients_a3 : boost::array< Value , 3 >
71         (*this)[0] = static_cast< Value >( 1 )/static_cast< Value >( 24 );  in rk78_coefficients_a3()
72         (*this)[1] = static_cast< Value >( 0 );  in rk78_coefficients_a3()
73         (*this)[2] = static_cast< Value >( 1 )/static_cast< Value >( 8 );  in rk78_coefficients_a3()
77 template< class Value = double >
78 struct rk78_coefficients_a4 : boost::array< Value , 4 >
82         (*this)[0] = static_cast< Value >( 5 )/static_cast< Value >( 12 );  in rk78_coefficients_a4()
83         (*this)[1] = static_cast< Value >( 0 );  in rk78_coefficients_a4()
84         (*this)[2] = static_cast< Value >( -25 )/static_cast< Value >( 16 );  in rk78_coefficients_a4()
85         (*this)[3] = static_cast< Value >( 25 )/static_cast< Value >( 16 );  in rk78_coefficients_a4()
89 template< class Value = double >
90 struct rk78_coefficients_a5 : boost::array< Value , 5 >
94         (*this)[0] = static_cast< Value >( 1 )/static_cast< Value >( 20 );  in rk78_coefficients_a5()
95         (*this)[1] = static_cast< Value >( 0 );  in rk78_coefficients_a5()
96         (*this)[2] = static_cast< Value >( 0 );  in rk78_coefficients_a5()
97         (*this)[3] = static_cast< Value >( 1 )/static_cast< Value >( 4 );  in rk78_coefficients_a5()
98         (*this)[4] = static_cast< Value >( 1 )/static_cast< Value >( 5 );  in rk78_coefficients_a5()
103 template< class Value = double >
104 struct rk78_coefficients_a6 : boost::array< Value , 6 >
108         (*this)[0] = static_cast< Value >( -25 )/static_cast< Value >( 108 );  in rk78_coefficients_a6()
109         (*this)[1] = static_cast< Value >( 0 );  in rk78_coefficients_a6()
110         (*this)[2] = static_cast< Value >( 0 );  in rk78_coefficients_a6()
111         (*this)[3] = static_cast< Value >( 125 )/static_cast< Value >( 108 );  in rk78_coefficients_a6()
112         (*this)[4] = static_cast< Value >( -65 )/static_cast< Value >( 27 );  in rk78_coefficients_a6()
113         (*this)[5] = static_cast< Value >( 125 )/static_cast< Value >( 54 );  in rk78_coefficients_a6()
117 template< class Value = double >
118 struct rk78_coefficients_a7 : boost::array< Value , 7 >
122         (*this)[0] = static_cast< Value >( 31 )/static_cast< Value >( 300 );  in rk78_coefficients_a7()
123         (*this)[1] = static_cast< Value >( 0 );  in rk78_coefficients_a7()
124         (*this)[2] = static_cast< Value >( 0 );  in rk78_coefficients_a7()
125         (*this)[3] = static_cast< Value >( 0 );  in rk78_coefficients_a7()
126         (*this)[4] = static_cast< Value >( 61 )/static_cast< Value >( 225 );  in rk78_coefficients_a7()
127         (*this)[5] = static_cast< Value >( -2 )/static_cast< Value >( 9 );  in rk78_coefficients_a7()
128         (*this)[6] = static_cast< Value >( 13 )/static_cast< Value >( 900 );  in rk78_coefficients_a7()
132 template< class Value = double >
133 struct rk78_coefficients_a8 : boost::array< Value , 8 >
137         (*this)[0] = static_cast< Value >( 2 );  in rk78_coefficients_a8()
138         (*this)[1] = static_cast< Value >( 0 );  in rk78_coefficients_a8()
139         (*this)[2] = static_cast< Value >( 0 );  in rk78_coefficients_a8()
140         (*this)[3] = static_cast< Value >( -53 )/static_cast< Value >( 6 );  in rk78_coefficients_a8()
141         (*this)[4] = static_cast< Value >( 704 )/static_cast< Value >( 45 );  in rk78_coefficients_a8()
142         (*this)[5] = static_cast< Value >( -107 )/static_cast< Value >( 9 );  in rk78_coefficients_a8()
143         (*this)[6] = static_cast< Value >( 67 )/static_cast< Value >( 90 );  in rk78_coefficients_a8()
144         (*this)[7] = static_cast< Value >( 3 );  in rk78_coefficients_a8()
148 template< class Value = double >
149 struct rk78_coefficients_a9 : boost::array< Value , 9 >
153         (*this)[0] = static_cast< Value >( -91 )/static_cast< Value >( 108 );  in rk78_coefficients_a9()
154         (*this)[1] = static_cast< Value >( 0 );  in rk78_coefficients_a9()
155         (*this)[2] = static_cast< Value >( 0 );  in rk78_coefficients_a9()
156         (*this)[3] = static_cast< Value >( 23 )/static_cast< Value >( 108 );  in rk78_coefficients_a9()
157         (*this)[4] = static_cast< Value >( -976 )/static_cast< Value >( 135 );  in rk78_coefficients_a9()
158         (*this)[5] = static_cast< Value >( 311 )/static_cast< Value >( 54 );  in rk78_coefficients_a9()
159         (*this)[6] = static_cast< Value >( -19 )/static_cast< Value >( 60 );  in rk78_coefficients_a9()
160         (*this)[7] = static_cast< Value >( 17 )/static_cast< Value >( 6 );  in rk78_coefficients_a9()
161         (*this)[8] = static_cast< Value >( -1 )/static_cast< Value >( 12 );  in rk78_coefficients_a9()
165 template< class Value = double >
166 struct rk78_coefficients_a10 : boost::array< Value , 10 >
170         (*this)[0] = static_cast< Value >( 2383 )/static_cast< Value >( 4100 );  in rk78_coefficients_a10()
171         (*this)[1] = static_cast< Value >( 0 );  in rk78_coefficients_a10()
172         (*this)[2] = static_cast< Value >( 0 );  in rk78_coefficients_a10()
173         (*this)[3] = static_cast< Value >( -341 )/static_cast< Value >( 164 );  in rk78_coefficients_a10()
174         (*this)[4] = static_cast< Value >( 4496 )/static_cast< Value >( 1025 );  in rk78_coefficients_a10()
175         (*this)[5] = static_cast< Value >( -301 )/static_cast< Value >( 82 );  in rk78_coefficients_a10()
176         (*this)[6] = static_cast< Value >( 2133 )/static_cast< Value >( 4100 );  in rk78_coefficients_a10()
177         (*this)[7] = static_cast< Value >( 45 )/static_cast< Value >( 82 );  in rk78_coefficients_a10()
178         (*this)[8] = static_cast< Value >( 45 )/static_cast< Value >( 164 );  in rk78_coefficients_a10()
179         (*this)[9] = static_cast< Value >( 18 )/static_cast< Value >( 41 );  in rk78_coefficients_a10()
183 template< class Value = double >
184 struct rk78_coefficients_a11 : boost::array< Value , 11 >
188         (*this)[0] = static_cast< Value >( 3 )/static_cast< Value >( 205 );  in rk78_coefficients_a11()
189         (*this)[1] = static_cast< Value >( 0 );  in rk78_coefficients_a11()
190         (*this)[2] = static_cast< Value >( 0 );  in rk78_coefficients_a11()
191         (*this)[3] = static_cast< Value >( 0 );  in rk78_coefficients_a11()
192         (*this)[4] = static_cast< Value >( 0 );  in rk78_coefficients_a11()
193         (*this)[5] = static_cast< Value >( -6 )/static_cast< Value >( 41 );  in rk78_coefficients_a11()
194         (*this)[6] = static_cast< Value >( -3 )/static_cast< Value >( 205 );  in rk78_coefficients_a11()
195         (*this)[7] = static_cast< Value >( -3 )/static_cast< Value >( 41 );  in rk78_coefficients_a11()
196         (*this)[8] = static_cast< Value >( 3 )/static_cast< Value >( 41 );  in rk78_coefficients_a11()
197         (*this)[9] = static_cast< Value >( 6 )/static_cast< Value >( 41 );  in rk78_coefficients_a11()
198         (*this)[10] = static_cast< Value >( 0 );  in rk78_coefficients_a11()
202 template< class Value = double >
203 struct rk78_coefficients_a12 : boost::array< Value , 12 >
207         (*this)[0] = static_cast< Value >( -1777 )/static_cast< Value >( 4100 );  in rk78_coefficients_a12()
208         (*this)[1] = static_cast< Value >( 0 );  in rk78_coefficients_a12()
209         (*this)[2] = static_cast< Value >( 0 );  in rk78_coefficients_a12()
210         (*this)[3] = static_cast< Value >( -341 )/static_cast< Value >( 164 );  in rk78_coefficients_a12()
211         (*this)[4] = static_cast< Value >( 4496 )/static_cast< Value >( 1025 );  in rk78_coefficients_a12()
212         (*this)[5] = static_cast< Value >( -289 )/static_cast< Value >( 82 );  in rk78_coefficients_a12()
213         (*this)[6] = static_cast< Value >( 2193 )/static_cast< Value >( 4100 );  in rk78_coefficients_a12()
214         (*this)[7] = static_cast< Value >( 51 )/static_cast< Value >( 82 );  in rk78_coefficients_a12()
215         (*this)[8] = static_cast< Value >( 33 )/static_cast< Value >( 164 );  in rk78_coefficients_a12()
216         (*this)[9] = static_cast< Value >( 12 )/static_cast< Value >( 41 );  in rk78_coefficients_a12()
217         (*this)[10] = static_cast< Value >( 0 );  in rk78_coefficients_a12()
218         (*this)[11] = static_cast< Value >( 1 );  in rk78_coefficients_a12()
222 template< class Value = double >
223 struct rk78_coefficients_b : boost::array< Value , 13 >
227         (*this)[0] = static_cast< Value >( 0 );  in rk78_coefficients_b()
228         (*this)[1] = static_cast< Value >( 0 );  in rk78_coefficients_b()
229         (*this)[2] = static_cast< Value >( 0 );  in rk78_coefficients_b()
230         (*this)[3] = static_cast< Value >( 0 );  in rk78_coefficients_b()
231         (*this)[4] = static_cast< Value >( 0 );  in rk78_coefficients_b()
232         (*this)[5] = static_cast< Value >( 34 )/static_cast<Value>( 105 );  in rk78_coefficients_b()
233         (*this)[6] = static_cast< Value >( 9 )/static_cast<Value>( 35 );  in rk78_coefficients_b()
234         (*this)[7] = static_cast< Value >( 9 )/static_cast<Value>( 35 );  in rk78_coefficients_b()
235         (*this)[8] = static_cast< Value >( 9 )/static_cast<Value>( 280 );  in rk78_coefficients_b()
236         (*this)[9] = static_cast< Value >( 9 )/static_cast<Value>( 280 );  in rk78_coefficients_b()
237         (*this)[10] = static_cast< Value >( 0 );  in rk78_coefficients_b()
238         (*this)[11] = static_cast< Value >( 41 )/static_cast<Value>( 840 );  in rk78_coefficients_b()
239         (*this)[12] = static_cast< Value >( 41 )/static_cast<Value>( 840 );  in rk78_coefficients_b()
243 template< class Value = double >
244 struct rk78_coefficients_db : boost::array< Value , 13 >
248 …     (*this)[0] = static_cast< Value >( 0 ) - static_cast< Value >( 41 )/static_cast<Value>( 840 );  in rk78_coefficients_db()
249         (*this)[1] = static_cast< Value >( 0 );  in rk78_coefficients_db()
250         (*this)[2] = static_cast< Value >( 0 );  in rk78_coefficients_db()
251         (*this)[3] = static_cast< Value >( 0 );  in rk78_coefficients_db()
252         (*this)[4] = static_cast< Value >( 0 );  in rk78_coefficients_db()
253         (*this)[5] = static_cast< Value >( 0 );  in rk78_coefficients_db()
254         (*this)[6] = static_cast< Value >( 0 );  in rk78_coefficients_db()
255         (*this)[7] = static_cast< Value >( 0 );  in rk78_coefficients_db()
256         (*this)[8] = static_cast< Value >( 0 );  in rk78_coefficients_db()
257         (*this)[9] = static_cast< Value >( 0 );  in rk78_coefficients_db()
258 …    (*this)[10] = static_cast< Value >( 0 ) - static_cast< Value >( 41 )/static_cast<Value>( 840 );  in rk78_coefficients_db()
259         (*this)[11] = static_cast< Value >( 41 )/static_cast<Value>( 840 );  in rk78_coefficients_db()
260         (*this)[12] = static_cast< Value >( 41 )/static_cast<Value>( 840 );  in rk78_coefficients_db()
265 template< class Value = double >
266 struct rk78_coefficients_c : boost::array< Value , 13 >
270         (*this)[0] = static_cast< Value >( 0 );  in rk78_coefficients_c()
271         (*this)[1] = static_cast< Value >( 2 )/static_cast< Value >( 27 );  in rk78_coefficients_c()
272         (*this)[2] = static_cast< Value >( 1 )/static_cast< Value >( 9 );  in rk78_coefficients_c()
273         (*this)[3] = static_cast< Value >( 1 )/static_cast<Value>( 6 );  in rk78_coefficients_c()
274         (*this)[4] = static_cast< Value >( 5 )/static_cast<Value>( 12 );  in rk78_coefficients_c()
275         (*this)[5] = static_cast< Value >( 1 )/static_cast<Value>( 2 );  in rk78_coefficients_c()
276         (*this)[6] = static_cast< Value >( 5 )/static_cast<Value>( 6 );  in rk78_coefficients_c()
277         (*this)[7] = static_cast< Value >( 1 )/static_cast<Value>( 6 );  in rk78_coefficients_c()
278         (*this)[8] = static_cast< Value >( 2 )/static_cast<Value>( 3 );  in rk78_coefficients_c()
279         (*this)[9] = static_cast< Value >( 1 )/static_cast<Value>( 3 );  in rk78_coefficients_c()
280         (*this)[10] = static_cast< Value >( 1 );  in rk78_coefficients_c()
281         (*this)[11] = static_cast< Value >( 0 );  in rk78_coefficients_c()
282         (*this)[12] = static_cast< Value >( 1 );  in rk78_coefficients_c()
293 class Value = double ,
295 class Time = Value ,
301 class runge_kutta_fehlberg78 : public explicit_error_generic_rk< 13 , 8 , 8 , 7 , State , Value , D…
310     typedef explicit_error_generic_rk< 13 , 8 , 8 , 7 , State , Value , Deriv , Time ,
329 …fusion::make_vector( rk78_coefficients_a1<Value>() , rk78_coefficients_a2<Value>() , rk78_coeffici…  in runge_kutta_fehlberg78()
330 …    rk78_coefficients_a4<Value>() , rk78_coefficients_a5<Value>() , rk78_coefficients_a6<Value>() ,  in runge_kutta_fehlberg78()
331 …    rk78_coefficients_a7<Value>() , rk78_coefficients_a8<Value>() , rk78_coefficients_a9<Value>() ,  in runge_kutta_fehlberg78()
332 …rk78_coefficients_a10<Value>() , rk78_coefficients_a11<Value>() , rk78_coefficients_a12<Value>() )…  in runge_kutta_fehlberg78()
333 …rk78_coefficients_b<Value>() , rk78_coefficients_db<Value>() , rk78_coefficients_c<Value>() , alge…  in runge_kutta_fehlberg78()