Sufficient conditions of stability in calculations of stationary supersonic flows by a marching method and non-stationary viscous flows

In this paper the sufficient conditions of stability and monotony are received for calculations of supersonic stationary flows by a marching method. The sufficient conditions of stability are established also when constructing the explicit numerical schemes for solutions of non-stationary conservation lows with viscosity taken into account. The received conditions continuously transfer from a hyperbolic type of time step restrictions to parabolic ones as the viscosity coefficient increases.