diff options
| -rw-r--r-- | src/Makefile.am | 1 | ||||
| -rw-r--r-- | src/vZ.hpp | 1 | ||||
| -rw-r--r-- | src/vZ/Heun.hpp | 95 | ||||
| -rw-r--r-- | src/vZ/Integrator.hpp | 1 | ||||
| -rw-r--r-- | tests/Heun.cpp | 37 | ||||
| -rw-r--r-- | tests/Makefile.am | 2 |
6 files changed, 136 insertions, 1 deletions
diff --git a/src/Makefile.am b/src/Makefile.am index ff03023..9ad815b 100644 --- a/src/Makefile.am +++ b/src/Makefile.am @@ -19,6 +19,7 @@ nobase_include_HEADERS = vZ.hpp \ vZ/Euler.hpp \ + vZ/Heun.hpp \ vZ/Integrator.hpp \ vZ/Midpoint.hpp \ vZ/RK.hpp \ @@ -29,6 +29,7 @@ #include <vZ/Simple.hpp> #include <vZ/Euler.hpp> #include <vZ/Midpoint.hpp> +#include <vZ/Heun.hpp> #include <vZ/RK4.hpp> #endif // VZ_HPP diff --git a/src/vZ/Heun.hpp b/src/vZ/Heun.hpp new file mode 100644 index 0000000..b70df9e --- /dev/null +++ b/src/vZ/Heun.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_HEUN_HPP +#define VZ_HEUN_HPP + +namespace vZ +{ + // Heun's method + // + // Second order Runge-Kutta method + // Two function evaluations per step + // Its tableau is: + // + // 0 | + // 1 | 1 + // --+--------- + // | 1/2 1/2 + // + // k1 = dt*f(y[n]) + // k2 = dt*f(y[n] + dt*k1) + // y[n + 1] = y[n] + 1/2*(k1 + k2) + template <typename Y> + class GenericHeunIntegrator : public GenericSimpleIntegrator<Y> + { + public: + typedef typename GenericSimpleIntegrator<Y>::Scalar Scalar; + typedef typename GenericSimpleIntegrator<Y>::Function Function; + + GenericHeunIntegrator(Function f) + : GenericSimpleIntegrator<Y>(f, s_a, s_b) { } + ~GenericHeunIntegrator() { } + + 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 GenericHeunIntegrator<double> HeunIntegrator; + + // Implementation + + template <typename Y> + typename GenericHeunIntegrator<Y>::Scalar + GenericHeunIntegrator<Y>::s_a2Arr[1] = { + Scalar(1) + }; + + template <typename Y> + std::vector<typename GenericHeunIntegrator<Y>::Scalar> + GenericHeunIntegrator<Y>::s_aArr[1] = { + std::vector<Scalar>(s_a2Arr, s_a2Arr + 1) + }; + + template <typename Y> + typename GenericHeunIntegrator<Y>::ACoefficients + GenericHeunIntegrator<Y>::s_a(s_aArr, s_aArr + 1); + + template <typename Y> + typename GenericHeunIntegrator<Y>::Scalar + GenericHeunIntegrator<Y>::s_bArr[2] = { + Scalar(1)/Scalar(2), Scalar(1)/Scalar(2) + }; + + template <typename Y> + typename GenericHeunIntegrator<Y>::BCoefficients + GenericHeunIntegrator<Y>::s_b(s_bArr, s_bArr + 2); +} + +#endif // VZ_HEUN_HPP diff --git a/src/vZ/Integrator.hpp b/src/vZ/Integrator.hpp index 34bc870..9346eb8 100644 --- a/src/vZ/Integrator.hpp +++ b/src/vZ/Integrator.hpp @@ -82,5 +82,4 @@ namespace vZ } } - #endif // VZ_INTEGRATOR_HPP diff --git a/tests/Heun.cpp b/tests/Heun.cpp new file mode 100644 index 0000000..758524b --- /dev/null +++ b/tests/Heun.cpp @@ -0,0 +1,37 @@ +#include "vZ.hpp" +#include <cmath> +#include <cstdlib> +#include <iostream> +#include <iomanip> + +// y' = y (y == C*exp(t)) +double +f(double t, double y) +{ + return y; +} + +int +main() +{ + vZ::HeunIntegrator integrator(f); + integrator.y(1.0).x(0.0).h(0.02); + + integrator.integrate(2.0); + + double actual = integrator.y(); + double expected = std::exp(2.0); + + std::cout << std::setprecision(10) + << "Numerical: " << actual << std::endl + << "Expected: " << expected << std::endl; + + double error = std::fabs(expected - actual)/expected; + if (error > 1.4e-4) { + std::cerr << "Error: " << 100.0*error << "%" << std::endl; + return EXIT_FAILURE; + } else { + std::cout << "Error: " << 100.0*error << "%" << std::endl; + return EXIT_SUCCESS; + } +} diff --git a/tests/Makefile.am b/tests/Makefile.am index edef1ae..0baa463 100644 --- a/tests/Makefile.am +++ b/tests/Makefile.am @@ -21,9 +21,11 @@ INCLUDES = -I$(top_srcdir)/src check_PROGRAMS = Euler-test \ Midpoint-test \ + Heun-test \ RK4-test TESTS = $(check_PROGRAMS) Euler_test_SOURCES = Euler.cpp Midpoint_test_SOURCES = Midpoint.cpp +Heun_test_SOURCES = Heun.cpp RK4_test_SOURCES = RK4.cpp |