Stability of Implicit Difference Schemes with Space and Time-Dependent Coefficients

Abstract

A stability theorem is derived for implicit difference schemes approximating multidimensional initial-value problems for linear hyperbolic systems with variable coefficients, and lots of widely used difference schemes are proved to be stable under the conditions similar to those for the cases of constant coefficients. This theorem is an extension of the stability theorem due to Lax-Nirenberg. The proof is quite simple.