Convergence of spectral methods for Burgers' equation

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Abstract

In this paper, a general framework is presented for analyzing numerical methods for the evolutionary equations that admit semigroup formulations. This framework is then applied to spectral and pseudospectral methods for the Burgers' equation, using trigonometric, Chebyshev, and Legendre polynomials. Optimal order of convergence is obtained, which implies the spectral accuracy of these methods.

Original languageEnglish (US)
Pages (from-to)1520-1541
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume29
Issue number6
DOIs
StatePublished - 1992
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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