This paper describes an explicit spatial marching procedure for solving reduced Navier-Stokes equations. The equations are written for a computational space and the Jameson-Schmidt scheme is used for marching. The Vigneron technique of splitting the pressure term is used to account for the upstream influence in the boundary layers. This method is applied to compute a supersonic flow involving a shock reflection and a shock-boundary layer interaction. The computed results agree well with those of other investigators.