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/*************************************************************************
* Copyright (C) 2010 Tavian Barnes <tavianator@gmail.com> *
* *
* This file is part of The vZ Library. *
* *
* The vZ Library is free software; you can redistribute it and/or *
* modify it under the terms of the GNU Lesser General Public License as *
* published by the Free Software Foundation; either version 3 of the *
* License, or (at your option) any later version. *
* *
* The vZ Library is distributed in the hope that it will be useful, but *
* WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
* Lesser General Public License for more details. *
* *
* You should have received a copy of the GNU Lesser General Public *
* License along with this program. If not, see *
* <http://www.gnu.org/licenses/>. *
*************************************************************************/
#ifndef VZ_RKF45_HPP
#define VZ_RKF45_HPP
namespace vZ
{
// Runge-Kutta-Fehlberg method
//
// Fifth-order with embedded fourth-order
// Its tableau is:
//
// 0 |
// 1/4 | 1/4
// 3/8 | 3/32 9/34
// 12/13 | 1932/2197 -7200/2197 7296/2197
// 1 | 439/216 -8 3680/513 -845/4104
// 1/2 | -8/27 2 -3544/2565 1859/4104 -11/40
// ------+-----------------------------------------------------------
// b | 25/216 0 1408/2565 2197/4104 -1/5 0
// b* | 16/135 0 6656/12825 28561/56430 -9/50 2/55
template <typename Y>
class GenericRKF45Integrator : public GenericAdaptiveIntegrator<Y>
{
public:
typedef typename GenericAdaptiveIntegrator<Y>::Scalar Scalar;
typedef typename GenericAdaptiveIntegrator<Y>::Function Function;
GenericRKF45Integrator(Function f)
: GenericAdaptiveIntegrator<Y>(f, 5, s_a, s_b, s_bStar) { }
~GenericRKF45Integrator() { }
private:
typedef typename GenericAdaptiveIntegrator<Y>::ACoefficients ACoefficients;
typedef typename GenericAdaptiveIntegrator<Y>::BCoefficients BCoefficients;
static ACoefficients s_a;
static BCoefficients s_b;
static BCoefficients s_bStar;
static Scalar s_a2Arr[1];
static Scalar s_a3Arr[2];
static Scalar s_a4Arr[3];
static Scalar s_a5Arr[4];
static Scalar s_a6Arr[5];
static std::vector<Scalar> s_aArr[5];
static Scalar s_bArr[6];
static Scalar s_bStarArr[6];
};
// Type alias
typedef GenericRKF45Integrator<double> RKF45Integrator;
// Implementation
template <typename Y>
typename GenericRKF45Integrator<Y>::Scalar
GenericRKF45Integrator<Y>::s_a2Arr[1] = {
Scalar(1)/Scalar(4)
};
template <typename Y>
typename GenericRKF45Integrator<Y>::Scalar
GenericRKF45Integrator<Y>::s_a3Arr[2] = {
Scalar(3)/Scalar(32), Scalar(9)/Scalar(32)
};
template <typename Y>
typename GenericRKF45Integrator<Y>::Scalar
GenericRKF45Integrator<Y>::s_a4Arr[3] = {
Scalar(1932)/Scalar(2197),
-Scalar(7200)/Scalar(2197),
Scalar(7296)/Scalar(2197)
};
template <typename Y>
typename GenericRKF45Integrator<Y>::Scalar
GenericRKF45Integrator<Y>::s_a5Arr[4] = {
Scalar(439)/Scalar(216),
-Scalar(8),
Scalar(3680)/Scalar(513),
-Scalar(845)/Scalar(4104),
};
template <typename Y>
typename GenericRKF45Integrator<Y>::Scalar
GenericRKF45Integrator<Y>::s_a6Arr[5] = {
-Scalar(8)/Scalar(27),
Scalar(2),
-Scalar(3544)/Scalar(2565),
Scalar(1859)/Scalar(4104),
-Scalar(11)/Scalar(40)
};
template <typename Y>
std::vector<typename GenericRKF45Integrator<Y>::Scalar>
GenericRKF45Integrator<Y>::s_aArr[5] = {
std::vector<Scalar>(s_a2Arr, s_a2Arr + 1),
std::vector<Scalar>(s_a3Arr, s_a3Arr + 2),
std::vector<Scalar>(s_a4Arr, s_a4Arr + 3),
std::vector<Scalar>(s_a5Arr, s_a5Arr + 4),
std::vector<Scalar>(s_a6Arr, s_a6Arr + 5)
};
template <typename Y>
typename GenericRKF45Integrator<Y>::ACoefficients
GenericRKF45Integrator<Y>::s_a(s_aArr, s_aArr + 5);
template <typename Y>
typename GenericRKF45Integrator<Y>::Scalar
GenericRKF45Integrator<Y>::s_bArr[6] = {
Scalar(16)/Scalar(135),
Scalar(0),
Scalar(6656)/Scalar(12825),
Scalar(28561)/Scalar(56430),
-Scalar(9)/Scalar(50),
Scalar(2)/Scalar(55),
};
template <typename Y>
typename GenericRKF45Integrator<Y>::BCoefficients
GenericRKF45Integrator<Y>::s_b(s_bArr, s_bArr + 6);
template <typename Y>
typename GenericRKF45Integrator<Y>::Scalar
GenericRKF45Integrator<Y>::s_bStarArr[6] = {
Scalar(25)/Scalar(216),
Scalar(0),
Scalar(1408)/Scalar(2565),
Scalar(2197)/Scalar(4104),
-Scalar(1)/Scalar(5),
Scalar(0)
};
template <typename Y>
typename GenericRKF45Integrator<Y>::BCoefficients
GenericRKF45Integrator<Y>::s_bStar(s_bStarArr, s_bStarArr + 6);
}
#endif // VZ_RKF45_HPP
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