#include <stdio.h>
#include <math.h>

//dy/dt = -y(t)+ e^-t * cos(t)

double h, fx, fy;
double euler(double t0, double y0, double h, double(*f)(double , double ));
double f(double fx, double fy);
double der(double t, double y);
double sol(double t, double y);
double rk(double x0, double y0, double h, double(*f)(double , double ));
double error(double t0, double y0, double(*f)(double, double), double(*g)(double, double, double , double));

void main()
{
   // FILE *fi;
    int num;
    double t0 = 0;
    double y0 = 0;
    printf("state number of steps = ");
    scanf("%d", &num);
    printf("\nand their size =");
    scanf("%lf", &h);
   // fi = fopen("graph.xls", "w");
    for(int i = 0; i < num; i++)
    {
        y0 = rk(t0, y0, h, der);
        t0 += h;
        printf("y %d = %lf t %d = %lf",i,y0,i,t0);
        printf("error = %lf \n",fabs((sol(t0 + h, y0)-rk(t0, y0, h, der))/sol(t0 + h, y0)));
      //  fprintf(*fi,"%lf %lf %lf \n", t0, y0, fabs((sol(t0, y0)-rk(t0, y0, h, der))/rk(t0, y0, h, der)));
    }
    t0 = 0;
     for(int i = 0; i < num; i++)
    {
        y0 = euler(t0, y0, h, der);
        t0 += h;
        printf("y %d = %lf t %d = %lf ",i,y0,i,t0);
        printf("error = %lf \n",fabs((sol(t0 +h, y0)-euler(t0, y0, h, der))/sol(t0 + h, y0)));
    }

//tell it to draw graph in fi
  //   fclose(fi);
}

double euler(double t0, double y0, double h, double(*f)(double , double ))
{
   return y0 + h*f(t0, y0);
}

double der(double t, double y)
{
return -1*y + cos(t)* exp(-1*t);
}

double sol(double t, double y)
{
return sin(t)* exp(-1*t);
}

double rk(double t0, double y0, double h, double(*f)(double , double))
{
    double q1 = h * f(t0, y0);
    double q2 = h * f(t0 + h/2, y0 + q1/2);
    double q3 = h * f(t0 + h/2, y0 + q2/2);
    double q4 = h * f(t0 +h, y0 + q3);
    return y0 + (q1 + q2 + q3 + q4)/6;
}
/*
double error(double t0, double y0, double(*f)(double, double), double(*g)(double, double, double , double(*asd)(double t0, double y0))
{
return abs((f(t0, y0)- g(t0, y0, h, asd(t0, y0))/f(t0, y0));
}*/