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-rw-r--r--src/vZ.hpp1
-rw-r--r--src/vZ/RKF45.hpp154
-rw-r--r--tests/Makefile.am4
-rw-r--r--tests/RKF45.cpp39
4 files changed, 197 insertions, 1 deletions
diff --git a/src/vZ.hpp b/src/vZ.hpp
index 5aabd1c..7f72407 100644
--- a/src/vZ.hpp
+++ b/src/vZ.hpp
@@ -34,5 +34,6 @@
#include <vZ/Adaptive.hpp>
#include <vZ/HE12.hpp>
#include <vZ/BS23.hpp>
+#include <vZ/RKF45.hpp>
#endif // VZ_HPP
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
diff --git a/tests/Makefile.am b/tests/Makefile.am
index cab6d98..f6ad25e 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -24,7 +24,8 @@ check_PROGRAMS = Euler-test \
Heun-test \
RK4-test \
HE12-test \
- BS23-test
+ BS23-test \
+ RKF45-test
TESTS = $(check_PROGRAMS)
Euler_test_SOURCES = Euler.cpp
@@ -33,3 +34,4 @@ Heun_test_SOURCES = Heun.cpp
RK4_test_SOURCES = RK4.cpp
HE12_test_SOURCES = HE12.cpp
BS23_test_SOURCES = BS23.cpp
+RKF45_test_SOURCES = RKF45.cpp
diff --git a/tests/RKF45.cpp b/tests/RKF45.cpp
new file mode 100644
index 0000000..8b87216
--- /dev/null
+++ b/tests/RKF45.cpp
@@ -0,0 +1,39 @@
+#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::RKF45Integrator integrator(f);
+ integrator.tol(1e-6).y(1.0).x(0.0).h(0.06);
+
+ 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
+ << "h: " << integrator.h() << std::endl
+ << "rejections: " << integrator.rejections() << std::endl;
+
+ double error = std::fabs(expected - actual)/expected;
+ if (error > 1.5e-6) {
+ std::cerr << "Error: " << 100.0*error << "%" << std::endl;
+ return EXIT_FAILURE;
+ } else {
+ std::cout << "Error: " << 100.0*error << "%" << std::endl;
+ return EXIT_SUCCESS;
+ }
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-22 17:28:15 +0000