diff options
| -rw-r--r-- | src/Makefile.am | 1 | ||||
| -rw-r--r-- | src/vZ.hpp | 1 | ||||
| -rw-r--r-- | src/vZ/Midpoint.hpp | 95 | ||||
| -rw-r--r-- | tests/Makefile.am | 6 | ||||
| -rw-r--r-- | tests/Midpoint.cpp | 25 |
5 files changed, 126 insertions, 2 deletions
diff --git a/src/Makefile.am b/src/Makefile.am index 76c30b1..6cd2924 100644 --- a/src/Makefile.am +++ b/src/Makefile.am @@ -20,6 +20,7 @@ nobase_include_HEADERS = vZ.hpp \ vZ/Euler.hpp \ vZ/Integrator.hpp \ + vZ/Midpoint.hpp \ vZ/RK.hpp \ vZ/Simple.hpp \ vZ/Traits.hpp @@ -28,5 +28,6 @@ #include <vZ/RK.hpp> #include <vZ/Simple.hpp> #include <vZ/Euler.hpp> +#include <vZ/Midpoint.hpp> #endif // VZ_HPP diff --git a/src/vZ/Midpoint.hpp b/src/vZ/Midpoint.hpp new file mode 100644 index 0000000..3d7ce2c --- /dev/null +++ b/src/vZ/Midpoint.hpp @@ -0,0 +1,95 @@ +/************************************************************************* + * 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_MIDPOINT_HPP +#define VZ_MIDPOINT_HPP + +namespace vZ +{ + // Midpoint method + // + // Second order Runge-Kutta method + // Two function evaluations per step + // Its tableau is: + // + // 0 | + // 1/2|1/2 + // ---+----- + // |0 1 + // + // k1 = dt*f(y[n]) + // k2 = dt*f(y[n] + (dt/2)*k1) + // y[n + 1] = y[n] + k2 + template <typename Y> + class GenericMidpointIntegrator : public GenericSimpleIntegrator<Y> + { + public: + typedef typename GenericSimpleIntegrator<Y>::Scalar Scalar; + typedef typename GenericSimpleIntegrator<Y>::Function Function; + + GenericMidpointIntegrator(Function f) + : GenericSimpleIntegrator<Y>(f, s_a, s_b) { } + ~GenericMidpointIntegrator() { } + + 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 std::vector<Scalar> s_aArr[1]; + static Scalar s_bArr[2]; + }; + + // Type alias + typedef GenericMidpointIntegrator<double> MidpointIntegrator; + + // Implementation + + template <typename Y> + typename GenericMidpointIntegrator<Y>::Scalar + GenericMidpointIntegrator<Y>::s_a2Arr[1] = { + Scalar(1)/2 + }; + + template <typename Y> + std::vector<typename GenericMidpointIntegrator<Y>::Scalar> + GenericMidpointIntegrator<Y>::s_aArr[1] = { + std::vector<Scalar>(s_a2Arr, s_a2Arr + 1) + }; + + template <typename Y> + typename GenericMidpointIntegrator<Y>::ACoefficients + GenericMidpointIntegrator<Y>::s_a(s_aArr, s_aArr + 1); + + template <typename Y> + typename GenericMidpointIntegrator<Y>::Scalar + GenericMidpointIntegrator<Y>::s_bArr[2] = { + Scalar(0), Scalar(1) + }; + + template <typename Y> + typename GenericMidpointIntegrator<Y>::BCoefficients + GenericMidpointIntegrator<Y>::s_b(s_bArr, s_bArr + 2); +} + +#endif // VZ_MIDPOINT_HPP diff --git a/tests/Makefile.am b/tests/Makefile.am index a3d5a77..5f94aab 100644 --- a/tests/Makefile.am +++ b/tests/Makefile.am @@ -19,7 +19,9 @@ INCLUDES = -I$(top_srcdir)/src -check_PROGRAMS = Euler-test +check_PROGRAMS = Euler-test \ + Midpoint-test TESTS = $(check_PROGRAMS) -Euler_test_SOURCES = Euler.cpp +Euler_test_SOURCES = Euler.cpp +Midpoint_test_SOURCES = Midpoint.cpp diff --git a/tests/Midpoint.cpp b/tests/Midpoint.cpp new file mode 100644 index 0000000..aea1885 --- /dev/null +++ b/tests/Midpoint.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::MidpointIntegrator integrator(f); + integrator.y(1.0).x(0.0).h(0.02); + + integrator.integrate(2.0); + + std::cout << integrator.y() << std::endl + << std::exp(2.0) << std::endl; + + return EXIT_SUCCESS; +} |