Over the last ten years, robustness of schemes has raised an increasing interest among the CFD community. The objective of this article is to solve the quasi-one-dimensional compressible flow inside a “Shubin nozzle” and to investigate Bean-Warming and flux vector splitting methods for numerical solution of compressible flows. Two different conditions have been considered: first, there is a supersonic flow in the entry and a supersonic flow in the outlet, without any shock in the nozzle. Second, there is a supersonic flow in the inlet and a subsonic flow in the outlet of the nozzle and a shock occur inside the nozzle. The results show that the run time of the flux vector splitting scheme is more than the Bean-Warming scheme, and, the flux vector splitting scheme is more accurate than the Bean-Warming scheme. However the flux vector splitting scheme is more complicated.