Spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations

Zdzislaw Jackiewicz, B. Zubik-Kowal

Research output: Contribution to journalArticle

47 Scopus citations

Abstract

We investigate Chebyshev spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations. Waveform relaxation methods allow to replace the system of nonlinear differential equations resulting from the application of spectral collocation methods by a sequence of linear problems which can be effectively integrated in a parallel computing environment by highly stable implicit methods. The effectiveness of this approach is illustrated by numerical experiments on the Hutchinson's equation. The boundedness of waveform relaxation iterations is proved for the Hutchinson's equation. This result is used in the proof of the superlinear convergence of the iterations.

Original languageEnglish (US)
Pages (from-to)433-443
Number of pages11
JournalApplied Numerical Mathematics
Volume56
Issue number3-4 SPEC. ISS.
DOIs
StatePublished - Mar 1 2006

Keywords

  • Nonlinear partial delay differential equations
  • Pseudospectral methods
  • Waveform relaxation iterations

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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