Fehlberg45.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_FEHELBERG45_HH
#define SANDALS_FEHELBERG45_HH
 
#include <Sandals.hh>
#include <Sandals/RungeKutta.hh>
 
namespace Sandals
{
  template <typename Real>
  class Fehlberg45Tableau : public Tableau<Real, 6>
  {
  public:
    using typename Tableau<Real, 6>::Type;
    using typename Tableau<Real, 6>::Vector;
    using typename Tableau<Real, 6>::Matrix;

    Fehlberg45Tableau<Real>() {
      this->name        = "Fehlberg45";
      this->type        = Type::ERK;
      this->order       = 4;
      this->order_e     = 5;
      this->is_embedded = true;
      this->A   << 0.0,           0.0,            0.0,            0.0,           0.0,        0.0,
                   1.0/4.0,       0.0,            0.0,            0.0,           0.0,        0.0,
                   3.0/32.0,      9.0/32.0,       0.0,            0.0,           0.0,        0.0,
                   1932.0/2197.0, -7200.0/2197.0, 7296.0/2197.0,  0.0,           0.0,        0.0,
                   439.0/216.0,   -8.0,           3680.0/513.0,   -845.0/4104.0, 0.0,        0.0,
                   -8.0/27.0,     2.0,            -3544.0/2565.0, 1859.0/4104.0, -11.0/40.0, 0.0;
      this->b   << 25.0/216.0, 0.0,     1408.0/2565.0,  2197.0/4104.0,   -1.0/5.0,  0.0;
      this->b_e << 16.0/135.0, 0.0,     6656.0/12825.0, 28561.0/56430.0, -9.0/50.0, 2.0/55.0;
      this->c   << 0.0,        1.0/4.0, 3.0/8.0,        12.0/13.0,       1.0,       1.0/2.0;
    }
  }; // class Fehlberg45Tableau

  template <typename Real, Integer N, Integer M = 0>
  class Fehlberg45 : public RungeKutta<Real, 6, N, M>
  {
  public:
    using System = typename Implicit<Real, N, M>::Pointer; 

    Fehlberg45() : RungeKutta<Real, 6, N, M>(Fehlberg45Tableau<Real>()) {}

    Fehlberg45(System t_system) : RungeKutta<Real, 6, N, M>(Fehlberg45Tableau<Real>(), t_system) {}
 
  }; // class Fehlberg45
 
} // namespace Sandals
 
#endif // SANDALS_FEHELBERG45_HH