diff options
| -rw-r--r-- | src/Makefile.am | 1 | ||||
| -rw-r--r-- | src/vZ.hpp | 1 | ||||
| -rw-r--r-- | src/vZ/Midpoint.hpp | 2 | ||||
| -rw-r--r-- | src/vZ/RK.hpp | 2 | ||||
| -rw-r--r-- | src/vZ/RK4.hpp | 116 | ||||
| -rw-r--r-- | tests/Makefile.am | 4 | ||||
| -rw-r--r-- | tests/RK4.cpp | 25 |
7 files changed, 148 insertions, 3 deletions
diff --git a/src/Makefile.am b/src/Makefile.am index 6cd2924..ff03023 100644 --- a/src/Makefile.am +++ b/src/Makefile.am @@ -22,5 +22,6 @@ nobase_include_HEADERS = vZ.hpp \ vZ/Integrator.hpp \ vZ/Midpoint.hpp \ vZ/RK.hpp \ + vZ/RK4.hpp \ vZ/Simple.hpp \ vZ/Traits.hpp @@ -29,5 +29,6 @@ #include <vZ/Simple.hpp> #include <vZ/Euler.hpp> #include <vZ/Midpoint.hpp> +#include <vZ/RK4.hpp> #endif // VZ_HPP diff --git a/src/vZ/Midpoint.hpp b/src/vZ/Midpoint.hpp index 3d7ce2c..2329457 100644 --- a/src/vZ/Midpoint.hpp +++ b/src/vZ/Midpoint.hpp @@ -68,7 +68,7 @@ namespace vZ template <typename Y> typename GenericMidpointIntegrator<Y>::Scalar GenericMidpointIntegrator<Y>::s_a2Arr[1] = { - Scalar(1)/2 + Scalar(1)/Scalar(2) }; template <typename Y> diff --git a/src/vZ/RK.hpp b/src/vZ/RK.hpp index df608ff..a832779 100644 --- a/src/vZ/RK.hpp +++ b/src/vZ/RK.hpp @@ -69,7 +69,7 @@ namespace vZ i != a.end(); ++i) { - Scalar c = 0; + Scalar c(0); Y y = this->y(); for (typename std::vector<Scalar>::size_type j = 0; j < i->size(); ++j) { Scalar aij = i->at(j); diff --git a/src/vZ/RK4.hpp b/src/vZ/RK4.hpp new file mode 100644 index 0000000..fa50461 --- /dev/null +++ b/src/vZ/RK4.hpp @@ -0,0 +1,116 @@ +/************************************************************************* + * 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_RK4_HPP +#define VZ_RK4_HPP + +namespace vZ +{ + // RK4 method + // + // Fourth order Runge-Kutta method + // Four function evaluations per step + // Its tableau is: + // + // 0 | + // 1/2|1/2 + // 1/2|0 1/2 + // 1 |0 0 1 + // ---+--------------- + // |1/6 1/3 1/3 1/6 + // + // k1 = dt*f(y[n]) + // k2 = dt*f(y[n] + (dt/2)*k1) + // k3 = dt*f(y[n] + (dt/2)*k2) + // k4 = dt*f(y[n] + dt*k3) + // y[n + 1] = y[n] + (k1 + 2*k2 + 2*k3 + k4)/6 + template <typename Y> + class GenericRK4Integrator : public GenericSimpleIntegrator<Y> + { + public: + typedef typename GenericSimpleIntegrator<Y>::Scalar Scalar; + typedef typename GenericSimpleIntegrator<Y>::Function Function; + + GenericRK4Integrator(Function f) + : GenericSimpleIntegrator<Y>(f, s_a, s_b) { } + ~GenericRK4Integrator() { } + + private: + typedef typename GenericSimpleIntegrator<Y>::ACoefficients ACoefficients; + typedef typename GenericSimpleIntegrator<Y>::BCoefficients BCoefficients; + + static ACoefficients s_a; + static BCoefficients s_b; + + static Scalar s_a2Arr[1]; + static Scalar s_a3Arr[2]; + static Scalar s_a4Arr[3]; + static std::vector<Scalar> s_aArr[3]; + static Scalar s_bArr[4]; + }; + + // Type alias + typedef GenericRK4Integrator<double> RK4Integrator; + + // Implementation + + template <typename Y> + typename GenericRK4Integrator<Y>::Scalar + GenericRK4Integrator<Y>::s_a2Arr[1] = { + Scalar(1)/Scalar(2) + }; + template <typename Y> + typename GenericRK4Integrator<Y>::Scalar + GenericRK4Integrator<Y>::s_a3Arr[2] = { + Scalar(0), Scalar(1)/Scalar(2) + }; + template <typename Y> + typename GenericRK4Integrator<Y>::Scalar + GenericRK4Integrator<Y>::s_a4Arr[3] = { + Scalar(0), Scalar(0), Scalar(1) + }; + + template <typename Y> + std::vector<typename GenericRK4Integrator<Y>::Scalar> + GenericRK4Integrator<Y>::s_aArr[3] = { + std::vector<Scalar>(s_a2Arr, s_a2Arr + 1), + std::vector<Scalar>(s_a3Arr, s_a3Arr + 2), + std::vector<Scalar>(s_a4Arr, s_a4Arr + 3) + }; + + template <typename Y> + typename GenericRK4Integrator<Y>::ACoefficients + GenericRK4Integrator<Y>::s_a(s_aArr, s_aArr + 3); + + template <typename Y> + typename GenericRK4Integrator<Y>::Scalar + GenericRK4Integrator<Y>::s_bArr[4] = { + Scalar(1)/Scalar(6), + Scalar(1)/Scalar(3), + Scalar(1)/Scalar(3), + Scalar(1)/Scalar(6) + }; + + template <typename Y> + typename GenericRK4Integrator<Y>::BCoefficients + GenericRK4Integrator<Y>::s_b(s_bArr, s_bArr + 4); +} + +#endif // VZ_RK4_HPP diff --git a/tests/Makefile.am b/tests/Makefile.am index 5f94aab..edef1ae 100644 --- a/tests/Makefile.am +++ b/tests/Makefile.am @@ -20,8 +20,10 @@ INCLUDES = -I$(top_srcdir)/src check_PROGRAMS = Euler-test \ - Midpoint-test + Midpoint-test \ + RK4-test TESTS = $(check_PROGRAMS) Euler_test_SOURCES = Euler.cpp Midpoint_test_SOURCES = Midpoint.cpp +RK4_test_SOURCES = RK4.cpp diff --git a/tests/RK4.cpp b/tests/RK4.cpp new file mode 100644 index 0000000..8e0ca0a --- /dev/null +++ b/tests/RK4.cpp @@ -0,0 +1,25 @@ +#include "vZ.hpp" +#include <cmath> +#include <cstdlib> +#include <iostream> + +// y' = y (y == C*exp(t)) +double +f(double t, double y) +{ + return y; +} + +int +main() +{ + vZ::RK4Integrator integrator(f); + integrator.y(1.0).x(0.0).h(0.04); + + integrator.integrate(2.0); + + std::cout << integrator.y() << std::endl + << std::exp(2.0) << std::endl; + + return EXIT_SUCCESS; +} |