/* 
************************************************************************
*  euler.c: 1st order Euler solution for an ordinary differential
*           equation
************************************************************************
*/
       
#include <stdio.h>
#include <math.h>

#define MIN 0.0                               /* minimum x */
#define MAX 1.0                               /* maximum x */
#define PI 3.1415926
 
main()
{
   double f(double x, double y);
   
   double x, y, dx, dy, yreal, yerror;
   
   FILE *output;                           /* save data in euler.dat */
   output = fopen("euler.dat","w");
   
   printf("Input: dx\n");
   scanf("%lf", &dx);
   printf("dx=%g\n", dx);

   x = MIN;                                /* initial position  */
   y = 0.0;
   yreal = y;
   yerror = 0.0;

   fprintf(output, "%f\t%f\t%f\t%e\n", x, y, yreal, yerror);
   

   while(x <= MAX)
   {
      dy = dx*f(x, y);
      x += dx;
      y += dy;
      yreal=sin(2.0*PI*x);
      yerror=y-yreal;
      fprintf(output, "%f\t%f\t%f\t%e\n", x, y, yreal, yerror);
   }
   printf("data stored in euler.dat\n");
   fclose(output);
}
/*-----------------------end of main program--------------------------*/

/* definition of equations */
double  f(double x, double y)
{
   return(2.0*PI*cos(2.0*PI*x));               /* RHS of first equation */
}