program rk4prog

      real x,t,dt,k(4)

      dt = 0.25
      x = 1
      open(unit=13,file="data.d")

      do 10 t=0,20,dt
         write(13,*) t,x,exp(-sin(t)),exp(-sin(t))-x
         k(1) = -x*cos(t)*dt
         k(2) = -(x+0.5*k(1))*cos(t+0.5*dt)*dt
         k(3) = -(x+0.5*k(2))*cos(t+0.5*dt)*dt
         k(4) = -(x+k(3))*cos(t+dt)*dt
         x = x + 1.0/6.0*(k(1) + 2.0*k(2) + 2.0*k(3) + k(4))
 10   continue

      end