Open AccessZero-stability of waveform relaxation methods for ordinary differential equations
Author(s) -
Zhencheng Fan
Publication year - 2022
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2022060
Subject(s) - zero (linguistics) , ordinary differential equation , mathematics , waveform , stability (learning theory) , relaxation (psychology) , numerical stability , ode , mathematical analysis , lipschitz continuity , numerical methods for ordinary differential equations , differential equation , numerical analysis , physics , differential algebraic equation , computer science , psychology , social psychology , philosophy , linguistics , quantum mechanics , voltage , machine learning
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.