/*This file show main steps of Euler method for solving differential equation */ 
/* Complete the program and use it to solve 
d y / dt = - y +1
at t = 0, y = 0.0;
 
At the end, compare your answer with the analytical solution 
This can be done by plotting computed value of y as a function of t. On the same plot show analytical solution as a function 
of t.
*/




#include<stdio.h>
#include<math.h>
/* Right hand side of the Differential equation 
 d y/ dx = f(x, y)
*/
double func(double x, double y);
main()
{

FILE *fpt;
int N,n;
double x, x0, xMax, y0, y, h, ans, fun;
 
printf("\nEnter the upper limit of Integration: ");
scanf("%lf",&xMax);
printf("\nEnter a value for h: ");
scanf("%lf",&h);

fpt = fopen("answer.data","w");

y0 = 0;
x0 = 0;
N = (double) ((xMax - x0)/ h);
/* Make y equal to initial condition at x = x0; */
y= y0;
x = x0;

for(n= -1; n <= N; n++){
	fun = func( x, y);
	x =x+h;
/* Euler  update */
	y = y + h * fun;  
	fscanf(fpt,"%lf %lf %lf %lf",h, n, x, ans);
	fprintf(fpt,"%lf %lf  %lf %lf", h, n,x, ans);
	fprintf(stdout,"h =%.12lf  n=%.12lf		t=%.12lf		y=%.12lf\n",h,n,x,ans);
}
fclose(fpt);
}
/* Print your data to a file */
double func(double x, double y)
{
	double ans;
ans = -y +1;
return ans;
}