Zero-stability of waveform relaxation methods for ordinary differential equations

Abstract

Zero-stability is the basic property of numerical methods of ordinary differential equations (ODEs). Little work on zero-stability is obtained for the waveform relaxation (WR) methods, although it is an important numerical method of ODEs. In this paper we present a definition of zero-stability of WR methods and prove that several classes of WR methods are zero-stable under the Lipschitz conditions. Also, some numerical examples are given to outline the effectiveness of the developed results.

Keywords

• waveform relaxation methods
• zero stability
• ordinary differential equations
• linear multi-step methods
• lipschitz conditions