Under the frame of Euler equations and Beam Warming TVD scheme,three time derivative discretion methods,i.e.Beam Warming implicit approximative factorization algorithm,implicit subiteration algorithm and simplified Runge Kutta five stage scheme,are numerically tested for the early evolution of underexpanded free jet flow.The results show that (i)Beam Warming implicit approximative factorization algorithm can give reasonable patterns of flowfield in whole.Some detailed features should be further studied;(ii)Implicit subiteration scheme with first-order accuracy in time would result in some abnormal phenomena so that the accuracy may not be enough for the unsteady flow;(iii)The results computed by implicit subiteration scheme with second order accuracy in time are well in agreement with that by simplified Runge Kutta five stage scheme, so we can regard these two difference methods as feasible algorithms for unsteady flow computation.