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-rw-r--r--src/vZ/Midpoint.hpp95
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+/*************************************************************************
+ * 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_MIDPOINT_HPP
+#define VZ_MIDPOINT_HPP
+
+namespace vZ
+{
+ // Midpoint method
+ //
+ // Second order Runge-Kutta method
+ // Two function evaluations per step
+ // Its tableau is:
+ //
+ // 0 |
+ // 1/2|1/2
+ // ---+-----
+ // |0 1
+ //
+ // k1 = dt*f(y[n])
+ // k2 = dt*f(y[n] + (dt/2)*k1)
+ // y[n + 1] = y[n] + k2
+ template <typename Y>
+ class GenericMidpointIntegrator : public GenericSimpleIntegrator<Y>
+ {
+ public:
+ typedef typename GenericSimpleIntegrator<Y>::Scalar Scalar;
+ typedef typename GenericSimpleIntegrator<Y>::Function Function;
+
+ GenericMidpointIntegrator(Function f)
+ : GenericSimpleIntegrator<Y>(f, s_a, s_b) { }
+ ~GenericMidpointIntegrator() { }
+
+ 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 GenericMidpointIntegrator<double> MidpointIntegrator;
+
+ // Implementation
+
+ template <typename Y>
+ typename GenericMidpointIntegrator<Y>::Scalar
+ GenericMidpointIntegrator<Y>::s_a2Arr[1] = {
+ Scalar(1)/2
+ };
+
+ template <typename Y>
+ std::vector<typename GenericMidpointIntegrator<Y>::Scalar>
+ GenericMidpointIntegrator<Y>::s_aArr[1] = {
+ std::vector<Scalar>(s_a2Arr, s_a2Arr + 1)
+ };
+
+ template <typename Y>
+ typename GenericMidpointIntegrator<Y>::ACoefficients
+ GenericMidpointIntegrator<Y>::s_a(s_aArr, s_aArr + 1);
+
+ template <typename Y>
+ typename GenericMidpointIntegrator<Y>::Scalar
+ GenericMidpointIntegrator<Y>::s_bArr[2] = {
+ Scalar(0), Scalar(1)
+ };
+
+ template <typename Y>
+ typename GenericMidpointIntegrator<Y>::BCoefficients
+ GenericMidpointIntegrator<Y>::s_b(s_bArr, s_bArr + 2);
+}
+
+#endif // VZ_MIDPOINT_HPP