The exact region of stability for MacCormack scheme
The scheme of \textit{R. W. MacCormack} [The effect of viscosity in hypervelocity impact cratering, AIAA Paper No. 69-354 (1969)] for the two-dimensional scalar advection equation with constant coefficients is considered. Necessary and sufficient conditions for the stability of the scheme are derived by analyzing the amplifications factor using quantifier elimination technique.
scientific article; zbMATH DE number 895860