# include <cmath>
# include <iomanip>
# include <iostream>

using namespace std;

# include "rk2.hpp"

//****************************************************************************80

void rk2 ( double *dydt ( double x, double y[] ), 
  double tspan[2], double y0[], int n, int m, double t[], double y[] )

//****************************************************************************80
//
//  Purpose:
//
//    rk2() uses the Runge-Kutta order 2 explicit method to solve an ODE.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    13 November 2024
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    dydt: a function that evaluates the right hand side of the ODE.
//
//    double tspan[2]: contains the initial and final times.
//
//    double y0[m]: a column vector containing the initial condition.
//
//    int n: the number of steps to take.
//
//    int m: the number of variables.
//
//  Output:
//
//    double t[n+1], y[m*(n+1)]: the times and solution values.
//
{
  double dt;
  double *f;
  int i;
  int j;
  double tm;
  double *ym;

  ym = new double[m];

  dt = ( tspan[1] - tspan[0] ) / ( double ) ( n );

  t[0] = tspan[0];
  j = 0;
  for ( i = 0; i < m; i++ )
  {
    y[i+j*m] = y0[i];
  }

  for ( j = 0; j < n; j++ )
  {
    f = dydt ( t[j], y+j*m );
    tm = t[j] + 0.5 * dt;
    for ( i = 0; i < m; i++ )
    {
      ym[i] = y[i+j*m] + 0.5 * dt * f[i];
    }
    delete [] f;

    f = dydt ( tm, ym );
    t[j+1] = t[j] + dt;
    for ( i = 0; i < m; i++ )
    {
      y[i+(j+1)*m] = y[i+j*m] + dt * f[i];
    }
    delete [] f;
  }

  delete [] ym;

  return;
}