Harten solution for one-dimensional unsteady equation

In order to use the second-order 5-point difference scheme mentioned to compute the solution of one dimension unsteady equations of the direct reflection of the strong plane detonation wave meeting a solid wall barrier, in this paper, we technically construct the difference schemes of the boundary and sub-boundary of the problem, and deduce the auto-analogue analytic solutions of the initial value problem, and at the same time, we present a method for the singular property of the initial value problem, from which we can get a satisfactory computation result of this difficult problem. The difference scheme used in this paper to deal with the discontinuity problems of the shock wave are valuable and worth generalization.