program main
      implicit none
      real(8) x,v,f,t,dt,t_fin
      integer Nt,it
      real(8) m,k
      real(8) kx1,kx2,kx3,kx4,kv1,kv2,kv3,kv4

      t_fin=10d0
      Nt=100
      dt=t_fin/Nt
      m=1d0
      k=1d0

      t=0d0
      x=1d0
      v=0d0

      open(10,file='Newton_Runge_Kutta.dat')
      write(10,'(3e16.6E3)')t,x,v

      do it=1,Nt
        t=dt*it

        kx1=v
        kv1=-k/m*x

        kx2=v+kv1*dt/2
        kv2=-k/m*(x+kx1*dt/2)

        kx3=v+kv2*dt/2
        kv3=-k/m*(x+kx2*dt/2)

        kx4=v+kv3*dt
        kv4=-k/m*(x+kx3*dt)

        x=x+dt/6*(kx1+2*kx2+2*kx3+kx4)
        v=v+dt/6*(kv1+2*kv2+2*kv3+kv4)

        write(10,*)t,x,v

      end do

      close(10)

      end program main