From 39617c503faf08de1324516adc8ebb7150c218ca Mon Sep 17 00:00:00 2001
From: Tavian Barnes <tavianator@gmail.com>
Date: Wed, 6 Oct 2010 17:57:48 -0400
Subject: Add RK4.

---
 src/vZ/RK4.hpp | 116 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 116 insertions(+)
 create mode 100644 src/vZ/RK4.hpp

(limited to 'src/vZ/RK4.hpp')

diff --git a/src/vZ/RK4.hpp b/src/vZ/RK4.hpp
new file mode 100644
index 0000000..fa50461
--- /dev/null
+++ b/src/vZ/RK4.hpp
@@ -0,0 +1,116 @@
+/*************************************************************************
+ * 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_RK4_HPP
+#define VZ_RK4_HPP
+
+namespace vZ
+{
+  // RK4 method
+  //
+  // Fourth order Runge-Kutta method
+  // Four function evaluations per step
+  // Its tableau is:
+  //
+  //   0  |
+  //   1/2|1/2
+  //   1/2|0   1/2
+  //   1  |0   0   1
+  //   ---+---------------
+  //      |1/6 1/3 1/3 1/6
+  //
+  //    k1    = dt*f(y[n])
+  //    k2    = dt*f(y[n] + (dt/2)*k1)
+  //    k3    = dt*f(y[n] + (dt/2)*k2)
+  //    k4    = dt*f(y[n] + dt*k3)
+  // y[n + 1] = y[n] + (k1 + 2*k2 + 2*k3 + k4)/6
+  template <typename Y>
+  class GenericRK4Integrator : public GenericSimpleIntegrator<Y>
+  {
+  public:
+    typedef typename GenericSimpleIntegrator<Y>::Scalar   Scalar;
+    typedef typename GenericSimpleIntegrator<Y>::Function Function;
+
+    GenericRK4Integrator(Function f)
+      : GenericSimpleIntegrator<Y>(f, s_a, s_b) { }
+    ~GenericRK4Integrator() { }
+
+  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 Scalar s_a3Arr[2];
+    static Scalar s_a4Arr[3];
+    static std::vector<Scalar> s_aArr[3];
+    static Scalar s_bArr[4];
+  };
+
+  // Type alias
+  typedef GenericRK4Integrator<double> RK4Integrator;
+
+  // Implementation
+
+  template <typename Y>
+  typename GenericRK4Integrator<Y>::Scalar
+  GenericRK4Integrator<Y>::s_a2Arr[1] = {
+    Scalar(1)/Scalar(2)
+  };
+  template <typename Y>
+  typename GenericRK4Integrator<Y>::Scalar
+  GenericRK4Integrator<Y>::s_a3Arr[2] = {
+    Scalar(0), Scalar(1)/Scalar(2)
+  };
+  template <typename Y>
+  typename GenericRK4Integrator<Y>::Scalar
+  GenericRK4Integrator<Y>::s_a4Arr[3] = {
+    Scalar(0), Scalar(0), Scalar(1)
+  };
+
+  template <typename Y>
+  std::vector<typename GenericRK4Integrator<Y>::Scalar>
+  GenericRK4Integrator<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 GenericRK4Integrator<Y>::ACoefficients
+  GenericRK4Integrator<Y>::s_a(s_aArr, s_aArr + 3);
+
+  template <typename Y>
+  typename GenericRK4Integrator<Y>::Scalar
+  GenericRK4Integrator<Y>::s_bArr[4] = {
+    Scalar(1)/Scalar(6),
+    Scalar(1)/Scalar(3),
+    Scalar(1)/Scalar(3),
+    Scalar(1)/Scalar(6)
+  };
+
+  template <typename Y>
+  typename GenericRK4Integrator<Y>::BCoefficients
+  GenericRK4Integrator<Y>::s_b(s_bArr, s_bArr + 4);
+}
+
+#endif // VZ_RK4_HPP
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