Numerical Stability, Resolvent Conditions and Delay Differential Equations

摘要

This paper is concerned with step-by-step methods for the numerical solution oflinear initial value problems. It deals with initial value problems for differential equations without delay-term as well as with equations in which a delayed argument of the dependent variable occurs. Recently, new tools for stability analysis were developed that are related to the so-called resolved condition of Kriess. These tools can be used in proving stability. The purpose of this paper is to review, extend, and apply some of these recent results.