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2022, Volume 30, Issue 3: 1126-1141. doi: 10.3934/era.2022060
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Zero-stability of waveform relaxation methods for ordinary differential equations

  • College of Mathematics and Data Science, Minjiang University, Fuzhou 350108, China

  • Academic Editor:Jingzhi Li
  • Received: 09 October 2021 Revised: 18 January 2022 Accepted: 27 February 2022 Published: 11 March 2022

  • 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.

    Citation: Zhencheng Fan. Zero-stability of waveform relaxation methods for ordinary differential equations[J]. Electronic Research Archive, 2022, 30(3): 1126-1141. doi: 10.3934/era.2022060

    Related Papers:

  • 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.


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