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

Zdzislaw Jackiewicz, B. Zubik-Kowal

Research output: Contribution to journalArticle

2 Citations (Scopus)

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

Fingerprint

Waveform Relaxation Method
Collocation
Conservation Laws
Conservation
Differential equations
Implicit Method
Spectral Methods
Collocation Method
Chebyshev
Nonlinear Differential Equations
Smoothness
Experiments
Numerical Experiment
Numerical Solution
Interval

Keywords

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

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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