From f1983adb487bb531c1c68226596b26eebf99876a Mon Sep 17 00:00:00 2001
From: Tavian Barnes <tavianator@gmail.com>
Date: Wed, 6 Oct 2010 21:50:48 -0400
Subject: Add Heun-Euler adaptive method.

---
 src/vZ/HE12.hpp | 107 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 107 insertions(+)
 create mode 100644 src/vZ/HE12.hpp

(limited to 'src/vZ/HE12.hpp')

diff --git a/src/vZ/HE12.hpp b/src/vZ/HE12.hpp
new file mode 100644
index 0000000..0f7a299
--- /dev/null
+++ b/src/vZ/HE12.hpp
@@ -0,0 +1,107 @@
+/*************************************************************************
+ * 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
-- 
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