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Diffstat (limited to 'src/vZ')
| -rw-r--r-- | src/vZ/RKF45.hpp | 154 |
1 files changed, 154 insertions, 0 deletions
diff --git a/src/vZ/RKF45.hpp b/src/vZ/RKF45.hpp new file mode 100644 index 0000000..5d40b88 --- /dev/null +++ b/src/vZ/RKF45.hpp @@ -0,0 +1,154 @@ +/************************************************************************* + * Copyright (C) 2009-2010 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, 3, 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 |