Ralston4.hh

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *\
 * Copyright (c) 2025, Davide Stocco and Enrico Bertolazzi.                                      *
 *                                                                                               *
 * The Sandals project is distributed under the BSD 2-Clause License.                            *
 *                                                                                               *
 * Davide Stocco                                                               Enrico Bertolazzi *
 * University of Trento                                                     University of Trento *
 * e-mail: davide.stocco@unitn.it                             e-mail: enrico.bertolazzi@unitn.it *
\* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
 
#pragma once
 
#ifndef SANDALS_RALSTON4_HH
#define SANDALS_RALSTON4_HH
 
#include <Sandals.hh>
#include <Sandals/RungeKutta.hh>
 
namespace Sandals
{
  template <typename Real>
  class Ralston4Tableau : public Tableau<Real, 4>
  {
  public:
    using typename Tableau<Real, 4>::Type;
    using typename Tableau<Real, 4>::Vector;
    using typename Tableau<Real, 4>::Matrix;

    Ralston4Tableau<Real>() {
      this->name  = "Ralston4";
      this->type  = Type::ERK;
      this->order = 4;
      Real s_5{std::sqrt(5.0)};
      Real a_21{4.0/10.0};
      Real a_31{(357.0/256.0) * s_5 - 2889.0/1024.0};
      Real a_32{3785.0/1024.0 - (405.0/256.0) * s_5};
      Real a_41{(1047.0/3020.0) * s_5 - 673.0/1208.0};
      Real a_42{-975.0/2552.0 - (1523.0/1276.0) * s_5};
      Real a_43{93408.0/48169.0 + (203968.0/240845.0) * s_5};
      Real b_1{263.0/1812.0 + (2.0/151.0) * s_5};
      Real b_2{125.0/3828.0 - (250.0/957.0) * s_5};
      Real b_3{3426304.0/5924787.0 + (553984.0/1974929.0) * s_5};
      Real b_4{10.0/41.0 - (4.0/123.0) * s_5};
      Real c_2{2.0/5.0};
      Real c_3{7.0/8.0 - (3.0/16.0) * s_5};
      this->A << 0.0,  0.0,  0.0,  0.0,
                 a_21, 0.0,  0.0,  0.0,
                 a_31, a_32, 0.0,  0.0,
                 a_41, a_42, a_43, 0.0;
      this->b << b_1, b_2, b_3, b_4;
      this->c << 0.0, c_2, c_3, 1.0;
    }
  }; // class Ralston4Tableau

  template <typename Real, Integer N, Integer M = 0>
  class Ralston4 : public RungeKutta<Real, 4, N, M>
  {
  public:
    using System = typename Implicit<Real, N, M>::Pointer; 

    Ralston4() : RungeKutta<Real, 4, N, M>(Ralston4Tableau<Real>()) {}

    Ralston4(System t_system) : RungeKutta<Real, 4, N, M>(Ralston4Tableau<Real>(), t_system) {}
 
  }; // class Ralston4
 
} // namespace Sandals
 
#endif // SANDALS_RALSTON4_HH