From c9d71b99d4bf8c7eef40c043c8d7726962847667 Mon Sep 17 00:00:00 2001 From: Tavian Barnes Date: Thu, 7 Oct 2010 21:15:22 -0400 Subject: Add DP45 method. --- src/Makefile.am | 3 + src/vZ.hpp | 1 + src/vZ/DP45.hpp | 167 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 3 files changed, 171 insertions(+) create mode 100644 src/vZ/DP45.hpp (limited to 'src') diff --git a/src/Makefile.am b/src/Makefile.am index 42c9279..bf2b10c 100644 --- a/src/Makefile.am +++ b/src/Makefile.am @@ -20,6 +20,8 @@ nobase_include_HEADERS = vZ.hpp \ vZ/Adaptive.hpp \ vZ/BS23.hpp \ + vZ/CK45.hpp \ + vZ/DP45.hpp \ vZ/Euler.hpp \ vZ/HE12.hpp \ vZ/Heun.hpp \ @@ -27,5 +29,6 @@ nobase_include_HEADERS = vZ.hpp \ vZ/Midpoint.hpp \ vZ/RK.hpp \ vZ/RK4.hpp \ + vZ/RKF45.hpp \ vZ/Simple.hpp \ vZ/Traits.hpp diff --git a/src/vZ.hpp b/src/vZ.hpp index afce2d4..ab7b3c2 100644 --- a/src/vZ.hpp +++ b/src/vZ.hpp @@ -36,5 +36,6 @@ #include #include #include +#include #endif // VZ_HPP diff --git a/src/vZ/DP45.hpp b/src/vZ/DP45.hpp new file mode 100644 index 0000000..343bd72 --- /dev/null +++ b/src/vZ/DP45.hpp @@ -0,0 +1,167 @@ +/************************************************************************* + * Copyright (C) 2009-2010 Tavian Barnes * + * * + * 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 * + * . * + *************************************************************************/ + +#ifndef VZ_DP45_HPP +#define VZ_DP45_HPP + +namespace vZ +{ + // Dormand-Prince method + // + // Fifth-order with embedded fourth-order + // Its tableau is: + // + // 0 | + // 1/5 | 1/5 + // 3/10 | 3/40 9/40 + // 4/5 | 44/45 -56/15 32/9 + // 8/9 | 19372/6561 -25360/2186 64448/6561 -212/729 + // 1 | 9017/3168 -355/33 46732/5247 49/176 -5103/18656 + // 1 | 35/384 0 500/1113 125/192 -2187/6784 11/84 + // -----+------------------------------------------------------------------------ + // b | 35/384 0 500/1113 125/192 -2187/6784 11/84 0 + // b* | 5179/57600 0 7571/16695 393/640 -92097/339200 172/2100 1/40 + template + class GenericDP45Integrator : public GenericAdaptiveIntegrator + { + public: + typedef typename GenericAdaptiveIntegrator::Scalar Scalar; + typedef typename GenericAdaptiveIntegrator::Function Function; + + GenericDP45Integrator(Function f) + : GenericAdaptiveIntegrator(f, 5, s_a, s_b, s_bStar) { } + ~GenericDP45Integrator() { } + + private: + typedef typename GenericAdaptiveIntegrator::ACoefficients ACoefficients; + typedef typename GenericAdaptiveIntegrator::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 Scalar s_a7Arr[6]; + static std::vector s_aArr[6]; + static Scalar s_bArr[7]; + static Scalar s_bStarArr[7]; + }; + + // Type alias + typedef GenericDP45Integrator DP45Integrator; + + // Implementation + + template + typename GenericDP45Integrator::Scalar + GenericDP45Integrator::s_a2Arr[1] = { + Scalar(1)/Scalar(5) + }; + template + typename GenericDP45Integrator::Scalar + GenericDP45Integrator::s_a3Arr[2] = { + Scalar(3)/Scalar(40), Scalar(9)/Scalar(40) + }; + template + typename GenericDP45Integrator::Scalar + GenericDP45Integrator::s_a4Arr[3] = { + Scalar(44)/Scalar(45), -Scalar(56)/Scalar(15), Scalar(32)/Scalar(9) + }; + template + typename GenericDP45Integrator::Scalar + GenericDP45Integrator::s_a5Arr[4] = { + Scalar(19372)/Scalar(6561), + -Scalar(25360)/Scalar(2187), + Scalar(64448)/Scalar(6561), + -Scalar(212)/Scalar(729), + }; + template + typename GenericDP45Integrator::Scalar + GenericDP45Integrator::s_a6Arr[5] = { + Scalar(9017)/Scalar(3168), + -Scalar(355)/Scalar(33), + Scalar(46732)/Scalar(5247), + Scalar(49)/Scalar(176), + -Scalar(5103)/Scalar(18656) + }; + template + typename GenericDP45Integrator::Scalar + GenericDP45Integrator::s_a7Arr[6] = { + Scalar(35)/Scalar(384), + Scalar(0), + Scalar(500)/Scalar(1113), + Scalar(125)/Scalar(192), + -Scalar(2187)/Scalar(6784), + Scalar(11)/Scalar(84) + }; + + template + std::vector::Scalar> + GenericDP45Integrator::s_aArr[6] = { + std::vector(s_a2Arr, s_a2Arr + 1), + std::vector(s_a3Arr, s_a3Arr + 2), + std::vector(s_a4Arr, s_a4Arr + 3), + std::vector(s_a5Arr, s_a5Arr + 4), + std::vector(s_a6Arr, s_a6Arr + 5), + std::vector(s_a7Arr, s_a7Arr + 6) + }; + + template + typename GenericDP45Integrator::ACoefficients + GenericDP45Integrator::s_a(s_aArr, s_aArr + 6); + + template + typename GenericDP45Integrator::Scalar + GenericDP45Integrator::s_bArr[7] = { + Scalar(35)/Scalar(384), + Scalar(0), + Scalar(500)/Scalar(1113), + Scalar(125)/Scalar(192), + -Scalar(2187)/Scalar(6784), + Scalar(11)/Scalar(84), + Scalar(0) + }; + + template + typename GenericDP45Integrator::BCoefficients + GenericDP45Integrator::s_b(s_bArr, s_bArr + 7); + + template + typename GenericDP45Integrator::Scalar + GenericDP45Integrator::s_bStarArr[7] = { + Scalar(5179)/Scalar(57600), + Scalar(0), + Scalar(7571)/Scalar(16695), + Scalar(393)/Scalar(640), + -Scalar(92097)/Scalar(339200), + Scalar(187)/Scalar(2100), + Scalar(1)/Scalar(40) + }; + + template + typename GenericDP45Integrator::BCoefficients + GenericDP45Integrator::s_bStar(s_bStarArr, s_bStarArr + 7); +} + +#endif // VZ_DP45_HPP -- cgit v1.2.3