Linear Stability Analysis and Stability Regions in the Numerical Solution ofInitial Value Problems

摘要

This paper deals with the stability analysis of step-by-step methods in thenumerical solution of initial(-boundary) value problems. The focus is on problems involving linear, ordinary, and partial differential equations. Conditions are presented which guarantee the rate of error growth in the methods to be of moderate size. These conditions are related to the stability region of the method, and can be viewed as variants to the resolvent condition occurring in the famous Kreiss matrix theorem.