// Adams-Bashforth 4-step Explicit Method

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

#define F(t,y)   (-((y)+1.0)*((y)+3.0))
#define ExactF(t) (-3.0+2.0/(1.0+exp(-2*(t))))
#define t0     0.0
#define te     2.0
#define num    20.0

void main()
{
   double w[100], t;
   double h=(te-t0)/num;
   int i;

   t=t0+h*3.0;

   w[0]= -2.0;     // Runge-Kutta order 4로 구한 값들
   w[1]= -1.90033209;
   w[2]= -1.80262486;
   w[3]= -1.70868768;

   for(i=3; i<num; i++) {
      w[i+1]=w[i]+h/24.0*(55.0*F(t,w[i]) - 59.0*F(t-h,w[i-1])
	     + 37.0*F(t-2.0*h,w[i-2]) - 9.0*F(t-3.0*h,w[i-3]));
      t+=h;
   }

   printf(" ti         Exact           wi            Error\n");
   for(i=0; i<=num; i++)
      printf("%4.2f   %12.8f   %12.8f   %12.8e\n",
	 t0+h*i, ExactF(t0+h*i), w[i], fabs(ExactF(t0+h*i)-w[i]));

}