Differential equations, difference equations and matrix theory

Abstract

Priedrichs, in his studies of difference approxi- mations to solutions of symmetric hyperbolic systems, has shown that difference schemes with positive coefficients are stable. In this paper we show that this stability criterion of Priedrichs is valid for difference approximations to arbitrary hyperbolic systems. The proof relies on the convexity and monotonic ity of eigenvalues as matrix fvmctions over a linear space of matrices with only real eigenvalues.