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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_HE12_HPP
+#define VZ_HE12_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 GenericHE12Integrator : public GenericAdaptiveIntegrator<Y>
+ {
+ public:
+ typedef typename GenericAdaptiveIntegrator<Y>::Scalar Scalar;
+ typedef typename GenericAdaptiveIntegrator<Y>::Function Function;
+
+ GenericHE12Integrator(Function f)
+ : GenericAdaptiveIntegrator<Y>(f, 2, s_a, s_b, s_bStar) { }
+ ~GenericHE12Integrator() { }
+
+ 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 std::vector<Scalar> s_aArr[1];
+ static Scalar s_bArr[2];
+ static Scalar s_bStarArr[2];
+ };
+
+ // Type alias
+ typedef GenericHE12Integrator<double> HE12Integrator;
+
+ // Implementation
+
+ template <typename Y>
+ typename GenericHE12Integrator<Y>::Scalar
+ GenericHE12Integrator<Y>::s_a2Arr[1] = {
+ Scalar(1)
+ };
+
+ template <typename Y>
+ std::vector<typename GenericHE12Integrator<Y>::Scalar>
+ GenericHE12Integrator<Y>::s_aArr[1] = {
+ std::vector<Scalar>(s_a2Arr, s_a2Arr + 1)
+ };
+
+ template <typename Y>
+ typename GenericHE12Integrator<Y>::ACoefficients
+ GenericHE12Integrator<Y>::s_a(s_aArr, s_aArr + 1);
+
+ template <typename Y>
+ typename GenericHE12Integrator<Y>::Scalar
+ GenericHE12Integrator<Y>::s_bArr[2] = {
+ Scalar(1)/Scalar(2), Scalar(1)/Scalar(2)
+ };
+
+ template <typename Y>
+ typename GenericHE12Integrator<Y>::BCoefficients
+ GenericHE12Integrator<Y>::s_b(s_bArr, s_bArr + 2);
+
+ template <typename Y>
+ typename GenericHE12Integrator<Y>::Scalar
+ GenericHE12Integrator<Y>::s_bStarArr[2] = {
+ Scalar(1), Scalar(0)
+ };
+
+ template <typename Y>
+ typename GenericHE12Integrator<Y>::BCoefficients
+ GenericHE12Integrator<Y>::s_bStar(s_bStarArr, s_bStarArr + 2);
+}
+
+#endif // VZ_HE12_HPP