Stability of Gauss-Radau Pseudospectral Approximations of the One-Dimensional Wave Equation

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Abstract

We first extend the stability analysis. of pseudospectral approximations of the one-dimensional one-way wave equation ∂u/∂x = c(x) ∂u/∂x given in [11] to general Gauss-Radau collocation methods. We give asufficient condition on the collocation points for stability whichshows that classical Gauss-Radau ultraspherical methods are perfectly stable while their Gauss-Lobatto counterpart is not. When the stability condition is not met we introduce a simple modification of the approximation which leads to better stability properties. Numerical examples show that long term stability may substantially improve.

Original languageEnglish (US)
Pages (from-to)287-313
Number of pages27
JournalJournal of Scientific Computing
Volume18
Issue number2
DOIs
StatePublished - Apr 1 2003

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Keywords

  • Boundary conditions
  • Eigenvalues
  • Linear differential systems
  • Pseudospectral approximation
  • Stability
  • Wave equation

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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