c
c 3414 Summer 2002
c HW4, Problem 2(b)
c
      real   m, g, k
      common m, g, k

      m = 0.11
      g = -9.8
      k = 0.002

      read *, nsteps
      h = 2.0/nsteps
      vcur = 16.0

      print *, 'Taylor-2'
      do i = 1, nsteps
        vold = vcur
        tcur = h*i
        vcur = vold + h * (f(vold) + 0.5*h*ft(vold))
        print 1000, tcur, vcur
 1000   format(f4.1,f8.4)
      enddo
      stop
      end

      function f(v)
c
c Note that f() does not depend explicitly on t.
c
      real   m, g, k
      common m, g, k
      f = g - k*v*abs(v)/m
      return
      end

      function ft(v)
c
c Returns derivative of F with respect to t.
c
      real   m, g, k
      common m, g, k
      if (v.gt.0.0) then
        fv = -2.0*k*v/m
      else
        fv =  2.0*k*v/m
      endif
      ft = fv*f(v)
      return
      end