Spectral Collocation and Waveform Relaxation Methods with Gegenbauer Geconstruction for Nonlinear Conservation Laws

Zdzislaw Jackiewicz, B. Zubik-Kowal

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We investigate the Chebyshev spectral collocation and waveform relaxation methods for nonlinear conservation laws. 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 by highly stable implicit methods. The obtained numerical solution is then enhanced on the intervals of smoothness by the Gegenbauer reconstruction. The effectiveness of this approach is illustrated by numerical experiments.

Original languageEnglish (US)
Pages (from-to)51-71
Number of pages21
JournalComputational Methods in Applied Mathematics
Volume5
Issue number1
DOIs
StatePublished - 2005

Keywords

  • Gegenbauer Reconstruction
  • Nonlinear Conservation Law
  • Pseudospectral Methods
  • Waveform Relaxation Iterations

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Spectral Collocation and Waveform Relaxation Methods with Gegenbauer Geconstruction for Nonlinear Conservation Laws'. Together they form a unique fingerprint.

Cite this