Numerical stability, resolvent conditions and delay differential equations
The paper deals with the problem of estimating a priori the error growth in discretizations of linear initial value problems. Recently new tools for stability analysis were developed that are related to the so-called resolvent condition of Kreiss. The purpose of this paper is to review, extend and apply some of these recent stability estimates which are valid under the Kreiss resolvent condition under a strong version and a weak version thereof. An application of the Kreiss resolvent condition in the error growth analysis of numerical methods for delay differential equations is presented.
scientific article; zbMATH DE number 1036656
scientific article