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-rw-r--r--src/Makefile.am1
-rw-r--r--src/vZ.hpp1
-rw-r--r--src/vZ/Adaptive.hpp6
-rw-r--r--src/vZ/BS23.hpp127
-rw-r--r--tests/BS23.cpp39
-rw-r--r--tests/HE12.cpp11
-rw-r--r--tests/Makefile.am4
7 files changed, 182 insertions, 7 deletions
diff --git a/src/Makefile.am b/src/Makefile.am
index 04dabb8..42c9279 100644
--- a/src/Makefile.am
+++ b/src/Makefile.am
@@ -19,6 +19,7 @@
nobase_include_HEADERS = vZ.hpp \
vZ/Adaptive.hpp \
+ vZ/BS23.hpp \
vZ/Euler.hpp \
vZ/HE12.hpp \
vZ/Heun.hpp \
diff --git a/src/vZ.hpp b/src/vZ.hpp
index 9ce7beb..5aabd1c 100644
--- a/src/vZ.hpp
+++ b/src/vZ.hpp
@@ -33,5 +33,6 @@
#include <vZ/RK4.hpp>
#include <vZ/Adaptive.hpp>
#include <vZ/HE12.hpp>
+#include <vZ/BS23.hpp>
#endif // VZ_HPP
diff --git a/src/vZ/Adaptive.hpp b/src/vZ/Adaptive.hpp
index 74de0db..256bda6 100644
--- a/src/vZ/Adaptive.hpp
+++ b/src/vZ/Adaptive.hpp
@@ -41,6 +41,8 @@ namespace vZ
Scalar atol() const { return m_atol; }
Scalar rtol() const { return m_rtol; }
+ unsigned int rejections() const { return m_rejections; }
+
protected:
typedef typename GenericRKIntegrator<Y>::ACoefficients ACoefficients;
typedef typename GenericRKIntegrator<Y>::BCoefficients BCoefficients;
@@ -49,7 +51,7 @@ namespace vZ
GenericAdaptiveIntegrator(Function f, unsigned int order,
ACoefficients a, BCoefficients b,
BCoefficients bStar)
- : GenericRKIntegrator<Y>(f), m_order(order),
+ : GenericRKIntegrator<Y>(f), m_order(order), m_rejections(0),
m_a(a), m_b(b), m_bStar(bStar)
{ }
virtual ~GenericAdaptiveIntegrator() { }
@@ -59,6 +61,7 @@ namespace vZ
private:
Scalar m_atol, m_rtol;
unsigned int m_order;
+ unsigned int m_rejections;
ACoefficients m_a;
BCoefficients m_b, m_bStar;
};
@@ -94,6 +97,7 @@ namespace vZ
if (delta > scale) {
// Reject the step
this->h(newH);
+ ++m_rejections;
} else {
rejected = false;
}
diff --git a/src/vZ/BS23.hpp b/src/vZ/BS23.hpp
new file mode 100644
index 0000000..1092d81
--- /dev/null
+++ b/src/vZ/BS23.hpp
@@ -0,0 +1,127 @@
+/*************************************************************************
+ * 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_BS23_HPP
+#define VZ_BS23_HPP
+
+namespace vZ
+{
+ // Heun-Euler method
+ //
+ // Second-order with embedded first-order
+ // Its tableau is:
+ //
+ // 0 |
+ // 1 | 1
+ // --+---------
+ // | 1/2 1/2
+ // | 1 0
+ //
+ // 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 GenericBS23Integrator : public GenericAdaptiveIntegrator<Y>
+ {
+ public:
+ typedef typename GenericAdaptiveIntegrator<Y>::Scalar Scalar;
+ typedef typename GenericAdaptiveIntegrator<Y>::Function Function;
+
+ GenericBS23Integrator(Function f)
+ : GenericAdaptiveIntegrator<Y>(f, 3, s_a, s_b, s_bStar) { }
+ ~GenericBS23Integrator() { }
+
+ 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 std::vector<Scalar> s_aArr[3];
+ static Scalar s_bArr[4];
+ static Scalar s_bStarArr[4];
+ };
+
+ // Type alias
+ typedef GenericBS23Integrator<double> BS23Integrator;
+
+ // Implementation
+
+ template <typename Y>
+ typename GenericBS23Integrator<Y>::Scalar
+ GenericBS23Integrator<Y>::s_a2Arr[1] = {
+ Scalar(1)/Scalar(2)
+ };
+ template <typename Y>
+ typename GenericBS23Integrator<Y>::Scalar
+ GenericBS23Integrator<Y>::s_a3Arr[2] = {
+ Scalar(0), Scalar(3)/Scalar(4)
+ };
+ template <typename Y>
+ typename GenericBS23Integrator<Y>::Scalar
+ GenericBS23Integrator<Y>::s_a4Arr[3] = {
+ Scalar(2)/Scalar(9), Scalar(1)/Scalar(3), Scalar(4)/Scalar(9)
+ };
+
+ template <typename Y>
+ std::vector<typename GenericBS23Integrator<Y>::Scalar>
+ GenericBS23Integrator<Y>::s_aArr[3] = {
+ std::vector<Scalar>(s_a2Arr, s_a2Arr + 1),
+ std::vector<Scalar>(s_a3Arr, s_a3Arr + 2),
+ std::vector<Scalar>(s_a4Arr, s_a4Arr + 3)
+ };
+
+ template <typename Y>
+ typename GenericBS23Integrator<Y>::ACoefficients
+ GenericBS23Integrator<Y>::s_a(s_aArr, s_aArr + 3);
+
+ template <typename Y>
+ typename GenericBS23Integrator<Y>::Scalar
+ GenericBS23Integrator<Y>::s_bArr[4] = {
+ Scalar(2)/Scalar(9),
+ Scalar(1)/Scalar(3),
+ Scalar(4)/Scalar(9),
+ Scalar(0)
+ };
+
+ template <typename Y>
+ typename GenericBS23Integrator<Y>::BCoefficients
+ GenericBS23Integrator<Y>::s_b(s_bArr, s_bArr + 4);
+
+ template <typename Y>
+ typename GenericBS23Integrator<Y>::Scalar
+ GenericBS23Integrator<Y>::s_bStarArr[4] = {
+ Scalar(7)/Scalar(24),
+ Scalar(1)/Scalar(4),
+ Scalar(1)/Scalar(3),
+ Scalar(1)/Scalar(8)
+ };
+
+ template <typename Y>
+ typename GenericBS23Integrator<Y>::BCoefficients
+ GenericBS23Integrator<Y>::s_bStar(s_bStarArr, s_bStarArr + 4);
+}
+
+#endif // VZ_BS23_HPP
diff --git a/tests/BS23.cpp b/tests/BS23.cpp
new file mode 100644
index 0000000..15abd0c
--- /dev/null
+++ b/tests/BS23.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::BS23Integrator integrator(f);
+ integrator.tol(1e-6).y(1.0).x(0.0).h(0.03);
+
+ 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 > 4.8e-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/HE12.cpp b/tests/HE12.cpp
index 44d6943..511a8e0 100644
--- a/tests/HE12.cpp
+++ b/tests/HE12.cpp
@@ -23,16 +23,17 @@ main()
double expected = std::exp(2.0);
std::cout << std::setprecision(10)
- << "Numerical: " << actual << std::endl
- << "Expected: " << expected << std::endl
- << "h: " << integrator.h() << std::endl;
+ << "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 > 8.7e-7) {
- std::cerr << "Error: " << 100.0*error << "%" << std::endl;
+ std::cerr << "Error: " << 100.0*error << "%" << std::endl;
return EXIT_FAILURE;
} else {
- std::cout << "Error: " << 100.0*error << "%" << std::endl;
+ std::cout << "Error: " << 100.0*error << "%" << std::endl;
return EXIT_SUCCESS;
}
}
diff --git a/tests/Makefile.am b/tests/Makefile.am
index e3c7601..cab6d98 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -23,7 +23,8 @@ check_PROGRAMS = Euler-test \
Midpoint-test \
Heun-test \
RK4-test \
- HE12-test
+ HE12-test \
+ BS23-test
TESTS = $(check_PROGRAMS)
Euler_test_SOURCES = Euler.cpp
@@ -31,3 +32,4 @@ Midpoint_test_SOURCES = Midpoint.cpp
Heun_test_SOURCES = Heun.cpp
RK4_test_SOURCES = RK4.cpp
HE12_test_SOURCES = HE12.cpp
+BS23_test_SOURCES = BS23.cpp