Add Bogacki-Shampine method.

2 files changed, 132 insertions, 1 deletions

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