program ex043
C
C       This program solves the differential equation
C           dv/dt = g - alpha*v**2
C       by using the Euler method.
C
      implicit real*8(a-h,o-z)
C
      g=9.8d0
      alpha=0.1d0
c
      ti = 0.0d0            ! Initial value of t
      tf =10.0d0            ! Final   value of t
      vi = 0.0d0            ! Initial value of v
      n = 1000
      dt = (tf-ti)/n
C
      open(16,file='ex043.dat')     ! open(unit,file='filename')
C
      t = ti            ! Initial Conditions
      v = vi            ! Initial Conditions
      write(16,*) t, v
      do k = 1, n
          dv1 = f(v,g,alpha)*dt
          v1 = v + dv1/2    ! v' = v(k-1) + dt * f(v(k-1)) / 2
c
          dv = f(v1,g,alpha)*dt
          t = t + dt        ! t(k) = t(k-1) + dt
          v = v + dv        ! y(k) = y(k-1) + dt * f(v(k-1))
      write(16,*) t, v
      enddo
c
      stop
      end
c **********************************************************************
      function f(v,g,alpha)
c **********************************************************************
      implicit real*8 (a-h,o-z)
      f = g - alpha*v**2
      end