On the contractivity of implicit–explicit linear multistep methods

Abstract

This paper is concerned with the class of implicit-explicit linear multistep methods for the numerical solution of initial value problems for ordinary differential equations which are composed of stiff and nonstiff parts. We study the contractivity of such methods, with regard to linear autonomous systems of ordinary differential equations and a (scaled) Euclidean norm. In addition, we derive a strong stability result based on the stability regions of these methods.