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-rw-r--r--TODO2
-rw-r--r--src/Makefile.am3
-rw-r--r--src/vZ.hpp1
-rw-r--r--src/vZ/DP45.hpp167
-rw-r--r--tests/DP45.cpp40
-rw-r--r--tests/Makefile.am4
6 files changed, 216 insertions, 1 deletions
diff --git a/TODO b/TODO
new file mode 100644
index 0000000..6eded45
--- /dev/null
+++ b/TODO
@@ -0,0 +1,2 @@
+- Support systems of ODEs
+- Implement FSAL
diff --git a/src/Makefile.am b/src/Makefile.am
index 42c9279..bf2b10c 100644
--- a/src/Makefile.am
+++ b/src/Makefile.am
@@ -20,6 +20,8 @@
nobase_include_HEADERS = vZ.hpp \
vZ/Adaptive.hpp \
vZ/BS23.hpp \
+ vZ/CK45.hpp \
+ vZ/DP45.hpp \
vZ/Euler.hpp \
vZ/HE12.hpp \
vZ/Heun.hpp \
@@ -27,5 +29,6 @@ nobase_include_HEADERS = vZ.hpp \
vZ/Midpoint.hpp \
vZ/RK.hpp \
vZ/RK4.hpp \
+ vZ/RKF45.hpp \
vZ/Simple.hpp \
vZ/Traits.hpp
diff --git a/src/vZ.hpp b/src/vZ.hpp
index afce2d4..ab7b3c2 100644
--- a/src/vZ.hpp
+++ b/src/vZ.hpp
@@ -36,5 +36,6 @@
#include <vZ/BS23.hpp>
#include <vZ/RKF45.hpp>
#include <vZ/CK45.hpp>
+#include <vZ/DP45.hpp>
#endif // VZ_HPP
diff --git a/src/vZ/DP45.hpp b/src/vZ/DP45.hpp
new file mode 100644
index 0000000..343bd72
--- /dev/null
+++ b/src/vZ/DP45.hpp
@@ -0,0 +1,167 @@
+/*************************************************************************
+ * 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_DP45_HPP
+#define VZ_DP45_HPP
+
+namespace vZ
+{
+ // Dormand-Prince method
+ //
+ // Fifth-order with embedded fourth-order
+ // Its tableau is:
+ //
+ // 0 |
+ // 1/5 | 1/5
+ // 3/10 | 3/40 9/40
+ // 4/5 | 44/45 -56/15 32/9
+ // 8/9 | 19372/6561 -25360/2186 64448/6561 -212/729
+ // 1 | 9017/3168 -355/33 46732/5247 49/176 -5103/18656
+ // 1 | 35/384 0 500/1113 125/192 -2187/6784 11/84
+ // -----+------------------------------------------------------------------------
+ // b | 35/384 0 500/1113 125/192 -2187/6784 11/84 0
+ // b* | 5179/57600 0 7571/16695 393/640 -92097/339200 172/2100 1/40
+ template <typename Y>
+ class GenericDP45Integrator : public GenericAdaptiveIntegrator<Y>
+ {
+ public:
+ typedef typename GenericAdaptiveIntegrator<Y>::Scalar Scalar;
+ typedef typename GenericAdaptiveIntegrator<Y>::Function Function;
+
+ GenericDP45Integrator(Function f)
+ : GenericAdaptiveIntegrator<Y>(f, 5, s_a, s_b, s_bStar) { }
+ ~GenericDP45Integrator() { }
+
+ 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 Scalar s_a7Arr[6];
+ static std::vector<Scalar> s_aArr[6];
+ static Scalar s_bArr[7];
+ static Scalar s_bStarArr[7];
+ };
+
+ // Type alias
+ typedef GenericDP45Integrator<double> DP45Integrator;
+
+ // Implementation
+
+ template <typename Y>
+ typename GenericDP45Integrator<Y>::Scalar
+ GenericDP45Integrator<Y>::s_a2Arr[1] = {
+ Scalar(1)/Scalar(5)
+ };
+ template <typename Y>
+ typename GenericDP45Integrator<Y>::Scalar
+ GenericDP45Integrator<Y>::s_a3Arr[2] = {
+ Scalar(3)/Scalar(40), Scalar(9)/Scalar(40)
+ };
+ template <typename Y>
+ typename GenericDP45Integrator<Y>::Scalar
+ GenericDP45Integrator<Y>::s_a4Arr[3] = {
+ Scalar(44)/Scalar(45), -Scalar(56)/Scalar(15), Scalar(32)/Scalar(9)
+ };
+ template <typename Y>
+ typename GenericDP45Integrator<Y>::Scalar
+ GenericDP45Integrator<Y>::s_a5Arr[4] = {
+ Scalar(19372)/Scalar(6561),
+ -Scalar(25360)/Scalar(2187),
+ Scalar(64448)/Scalar(6561),
+ -Scalar(212)/Scalar(729),
+ };
+ template <typename Y>
+ typename GenericDP45Integrator<Y>::Scalar
+ GenericDP45Integrator<Y>::s_a6Arr[5] = {
+ Scalar(9017)/Scalar(3168),
+ -Scalar(355)/Scalar(33),
+ Scalar(46732)/Scalar(5247),
+ Scalar(49)/Scalar(176),
+ -Scalar(5103)/Scalar(18656)
+ };
+ template <typename Y>
+ typename GenericDP45Integrator<Y>::Scalar
+ GenericDP45Integrator<Y>::s_a7Arr[6] = {
+ Scalar(35)/Scalar(384),
+ Scalar(0),
+ Scalar(500)/Scalar(1113),
+ Scalar(125)/Scalar(192),
+ -Scalar(2187)/Scalar(6784),
+ Scalar(11)/Scalar(84)
+ };
+
+ template <typename Y>
+ std::vector<typename GenericDP45Integrator<Y>::Scalar>
+ GenericDP45Integrator<Y>::s_aArr[6] = {
+ 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),
+ std::vector<Scalar>(s_a7Arr, s_a7Arr + 6)
+ };
+
+ template <typename Y>
+ typename GenericDP45Integrator<Y>::ACoefficients
+ GenericDP45Integrator<Y>::s_a(s_aArr, s_aArr + 6);
+
+ template <typename Y>
+ typename GenericDP45Integrator<Y>::Scalar
+ GenericDP45Integrator<Y>::s_bArr[7] = {
+ Scalar(35)/Scalar(384),
+ Scalar(0),
+ Scalar(500)/Scalar(1113),
+ Scalar(125)/Scalar(192),
+ -Scalar(2187)/Scalar(6784),
+ Scalar(11)/Scalar(84),
+ Scalar(0)
+ };
+
+ template <typename Y>
+ typename GenericDP45Integrator<Y>::BCoefficients
+ GenericDP45Integrator<Y>::s_b(s_bArr, s_bArr + 7);
+
+ template <typename Y>
+ typename GenericDP45Integrator<Y>::Scalar
+ GenericDP45Integrator<Y>::s_bStarArr[7] = {
+ Scalar(5179)/Scalar(57600),
+ Scalar(0),
+ Scalar(7571)/Scalar(16695),
+ Scalar(393)/Scalar(640),
+ -Scalar(92097)/Scalar(339200),
+ Scalar(187)/Scalar(2100),
+ Scalar(1)/Scalar(40)
+ };
+
+ template <typename Y>
+ typename GenericDP45Integrator<Y>::BCoefficients
+ GenericDP45Integrator<Y>::s_bStar(s_bStarArr, s_bStarArr + 7);
+}
+
+#endif // VZ_DP45_HPP
diff --git a/tests/DP45.cpp b/tests/DP45.cpp
new file mode 100644
index 0000000..5faa78a
--- /dev/null
+++ b/tests/DP45.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::DP45Integrator 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 > 6.0e-7) {
+ 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 60e5cf3..5874419 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -26,7 +26,8 @@ check_PROGRAMS = Euler-test \
HE12-test \
BS23-test \
RKF45-test \
- CK45-test
+ CK45-test \
+ DP45-test
TESTS = $(check_PROGRAMS)
Euler_test_SOURCES = Euler.cpp
@@ -37,3 +38,4 @@ HE12_test_SOURCES = HE12.cpp
BS23_test_SOURCES = BS23.cpp
RKF45_test_SOURCES = RKF45.cpp
CK45_test_SOURCES = CK45.cpp
+DP45_test_SOURCES = DP45.cpp
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-21 20:00:21 +0000