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-rw-r--r--src/vZ.hpp1
-rw-r--r--src/vZ/CK45.hpp154
-rw-r--r--tests/CK45.cpp40
-rw-r--r--tests/Makefile.am4
4 files changed, 198 insertions, 1 deletions
diff --git a/src/vZ.hpp b/src/vZ.hpp
index 7f72407..afce2d4 100644
--- a/src/vZ.hpp
+++ b/src/vZ.hpp
@@ -35,5 +35,6 @@
#include <vZ/HE12.hpp>
#include <vZ/BS23.hpp>
#include <vZ/RKF45.hpp>
+#include <vZ/CK45.hpp>
#endif // VZ_HPP
diff --git a/src/vZ/CK45.hpp b/src/vZ/CK45.hpp
new file mode 100644
index 0000000..333e451
--- /dev/null
+++ b/src/vZ/CK45.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_CK45_HPP
+#define VZ_CK45_HPP
+
+namespace vZ
+{
+ // Cash-Karp method
+ //
+ // Fifth-order with embedded fourth-order
+ // Its tableau is:
+ //
+ // 0 |
+ // 1/5 | 1/5
+ // 3/10 | 3/40 9/40
+ // 3/5 | 3/10 -9/10 6/5
+ // 1 | -11/54 5/2 -70/27 35/27
+ // 7/8 | 1631/55296 175/512 575/13824 44275/110592 253/4096
+ // ------+-----------------------------------------------------------------
+ // b | 37/378 0 250/621 125/594 0 512/1771
+ // b* | 2825/27648 0 18575/48384 13525/55296 277/14336 1/4
+ template <typename Y>
+ class GenericCK45Integrator : public GenericAdaptiveIntegrator<Y>
+ {
+ public:
+ typedef typename GenericAdaptiveIntegrator<Y>::Scalar Scalar;
+ typedef typename GenericAdaptiveIntegrator<Y>::Function Function;
+
+ GenericCK45Integrator(Function f)
+ : GenericAdaptiveIntegrator<Y>(f, 5, s_a, s_b, s_bStar) { }
+ ~GenericCK45Integrator() { }
+
+ 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 GenericCK45Integrator<double> CK45Integrator;
+
+ // Implementation
+
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::Scalar
+ GenericCK45Integrator<Y>::s_a2Arr[1] = {
+ Scalar(1)/Scalar(5)
+ };
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::Scalar
+ GenericCK45Integrator<Y>::s_a3Arr[2] = {
+ Scalar(3)/Scalar(40), Scalar(9)/Scalar(40)
+ };
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::Scalar
+ GenericCK45Integrator<Y>::s_a4Arr[3] = {
+ Scalar(3)/Scalar(10),
+ -Scalar(9)/Scalar(10),
+ Scalar(6)/Scalar(5)
+ };
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::Scalar
+ GenericCK45Integrator<Y>::s_a5Arr[4] = {
+ -Scalar(11)/Scalar(54),
+ Scalar(5)/Scalar(2),
+ -Scalar(70)/Scalar(27),
+ Scalar(35)/Scalar(27),
+ };
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::Scalar
+ GenericCK45Integrator<Y>::s_a6Arr[5] = {
+ Scalar(1631)/Scalar(55296),
+ Scalar(175)/Scalar(512),
+ Scalar(575)/Scalar(13824),
+ Scalar(44275)/Scalar(110592),
+ Scalar(253)/Scalar(4096)
+ };
+
+ template <typename Y>
+ std::vector<typename GenericCK45Integrator<Y>::Scalar>
+ GenericCK45Integrator<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 GenericCK45Integrator<Y>::ACoefficients
+ GenericCK45Integrator<Y>::s_a(s_aArr, s_aArr + 5);
+
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::Scalar
+ GenericCK45Integrator<Y>::s_bArr[6] = {
+ Scalar(37)/Scalar(378),
+ Scalar(0),
+ Scalar(250)/Scalar(621),
+ Scalar(125)/Scalar(594),
+ Scalar(0),
+ Scalar(512)/Scalar(1771),
+ };
+
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::BCoefficients
+ GenericCK45Integrator<Y>::s_b(s_bArr, s_bArr + 6);
+
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::Scalar
+ GenericCK45Integrator<Y>::s_bStarArr[6] = {
+ Scalar(2825)/Scalar(27648),
+ Scalar(0),
+ Scalar(18575)/Scalar(48384),
+ Scalar(13525)/Scalar(55296),
+ Scalar(277)/Scalar(14336),
+ Scalar(1)/Scalar(4)
+ };
+
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::BCoefficients
+ GenericCK45Integrator<Y>::s_bStar(s_bStarArr, s_bStarArr + 6);
+}
+
+#endif // VZ_CK45_HPP
diff --git a/tests/CK45.cpp b/tests/CK45.cpp
new file mode 100644
index 0000000..e726bc6
--- /dev/null
+++ b/tests/CK45.cpp
@@ -0,0 +1,40 @@
+#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::CK45Integrator 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
+ << "Iterations: " << integrator.iterations() << std::endl
+ << "Rejections: " << integrator.rejections() << std::endl;
+
+ double error = std::fabs(expected - actual)/expected;
+ if (error > 2.7e-6) {
+ 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 f6ad25e..60e5cf3 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -25,7 +25,8 @@ check_PROGRAMS = Euler-test \
RK4-test \
HE12-test \
BS23-test \
- RKF45-test
+ RKF45-test \
+ CK45-test
TESTS = $(check_PROGRAMS)
Euler_test_SOURCES = Euler.cpp
@@ -35,3 +36,4 @@ RK4_test_SOURCES = RK4.cpp
HE12_test_SOURCES = HE12.cpp
BS23_test_SOURCES = BS23.cpp
RKF45_test_SOURCES = RKF45.cpp
+CK45_test_SOURCES = CK45.cpp
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-21 21:07:09 +0000