RadauIIA5.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_RADAUIIA5_HH
#define SANDALS_RADAUIIA5_HH
 
#include <Sandals.hh>
#include <Sandals/RungeKutta.hh>
 
namespace Sandals
{
  template <typename Real>
  class RadauIIA5Tableau : public Tableau<Real, 3>
  {
  public:
    using typename Tableau<Real, 3>::Type;
    using typename Tableau<Real, 3>::Vector;
    using typename Tableau<Real, 3>::Matrix;

    RadauIIA5Tableau<Real>() {
      this->name  = "RadauIIA5";
      this->type  = Type::IRK;
      this->order = 5;
      Real s6{std::sqrt(6.0)};
      this->A << 11.0/45.0-7.0*s6/360.0,   37.0/225.0-169.0*s6/1800.0, -2.0/225.0+s6/75.0,
                 37.0/225+169.0*s6/1800.0, 11.0/45.0+7.0*s6/360.0,     -2.0/225.0-s6/75.0,
                 4.0/9.0-s6/36.0,          4.0/9.0+s6/36.0,            1.0/9.0;
      this->b << 4.0/9.0-s6/36.0, 4.0/9.0+s6/36, 1.0/9.0;
      this->c << 2.0/5.0-s6/10.0, 2.0/5.0+s6/10, 1.0;
    }
  }; // class RadauIIA5Tableau

  template <typename Real, Integer N, Integer M = 0>
  class RadauIIA5 : public RungeKutta<Real, 3, N, M>
  {
  public:
    using System = typename Implicit<Real, N, M>::Pointer; 

    RadauIIA5() : RungeKutta<Real, 3, N, M>(RadauIIA5Tableau<Real>()) {}

    RadauIIA5(System t_system) : RungeKutta<Real, 3, N, M>(RadauIIA5Tableau<Real>(), t_system) {}
 
  }; // class RadauIIA5
 
} // namespace Sandals
 
#endif // SANDALS_RADAUIIA5_HH