# include <stdio.h>
# include <stdlib.h>

# include "rk1.h"

/******************************************************************************/

void rk1 ( void dydt ( double x, double y[], double yp[] ), double tspan[2], 
  double y0[], int n, int m, double t[], double y[] )

/******************************************************************************/
/*
  Purpose:

    rk1() solves an ODE using an explicit Runge-Kutta method of order 1.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    12 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 *dy;
  int i;
  int j;
  double tfirst;
  double tlast;

  dy = ( double * ) malloc ( m * sizeof ( double ) );

  tfirst = tspan[0];
  tlast = tspan[1];
  dt = ( tlast - tfirst ) / ( double ) ( n );
  j = 0;
  t[j] = tspan[0];
  for ( i = 0; i < m; i++ )
  {
    y[i+j*m] = y0[i];
  }

  for ( j = 0; j < n; j++ )
  {
    dydt ( t[j], y+j*m, dy );
    t[j+1] = t[j] + dt;
    for ( i = 0; i < m; i++ )
    {
      y[i+(j+1)*m] = y[i+j*m] + dt * dy[i];
    }
  }

  free ( dy );

  return;
}