program rk4ex

      real x1,x2,f1,f2,k1,k2,k3,k4,m1,m2,m3,m4
      dt = 1.25/2.0

      x1 = 0
      x2 = 0
      open(13,file="data.d")

      do 10 t=0,25,dt
         write(13,20) t,x1,x2,0.5*t*sin(t),0.5*t*sin(t)-x1

         k1 = f1(x1, x2, t)*dt
         m1 = f2(x1, x2,t)*dt

         k2 = f1(x1+0.5*k1, x2+0.5*m1, t+0.5*dt)*dt
         m2 = f2(x1+0.5*k1, x2+0.5*m1, t+0.5*dt)*dt

         k3 = f1(x1+0.5* k2,x2+0.5*m2, t+0.5*dt)*dt
         m3 = f2(x1+0.5* k2,x2+0.5*m2, t+0.5*dt)*dt

         k4 = f1(x1+k3, x2+m3, t+dt)*dt
         m4 = f2(x1+k3, x2+m3, t+dt)*dt

         x1 = x1 + 1.0/6.0*(k1+2*k2+2*k3+k4)
         x2 = x2 + 1.0/6.0*(m1+2*m2+2*m3+m4)

 10   continue
 20   format(5(F12.4))
      end

      real function f1(x1,x2,t)
      real x1,x2,t
      f1 = x2
      return
      end

      real function f2(x1,x2,t)
      real x1,x2,t
      f2 = -x1+cos(t)
      return
      end