A Numerical Algorithm for Stability Analysis of Difference Methods for Hyperbolic Systems

Abstract

The stability theory for difference approximations of hyperbolic initial boundary value problems is based on normal mode analysis. To perform such a stability investigation analytically is very difficult even for low-order approximations of scalar problems. For more complicated cases some numerical technique must be used. Here, a numerical algorithm designed for this purpose is presented. It can handle one- and two-dimensional problems and can easily be extended to higher-dimensional cases. The algorithm is justified by a theoretical analysis and experiments show that it is reliable and efficient.