@article{Fan2022, 
author = {Zhencheng Fan},
title = {Zero-stability of waveform relaxation methods for ordinary differential equations},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {3},
pages = {1126-1141},
keywords = {ordinary differential equations, Lipschitz conditions, waveform relaxation methods, zero stability, linear multi-step methods},
url = {https://www.sciopen.com/article/10.3934/era.2022060},
doi = {10.3934/era.2022060},
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.}
}