An adaptive pseudo-spectral method for reaction diffusion problems

A. Bayliss*, D. Gottlieb, B. J. Matkowsky, M. Minkoff

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

57 Scopus citations


We consider the spectral interpolation error for both Chebyshev pseudo-spectral and Galerkin approximations. We develop a family of functionals Ir(u), with the property that the maximum norm of the error is bounded by Ir(u)/Jr, where r is an integer and J is the degree of the polynomial approximation. These functionals are used in an adaptive procedure whereby the problem is dynamically transformed to minimize Ir(u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions.

Original languageEnglish (US)
Pages (from-to)421-443
Number of pages23
JournalJournal of Computational Physics
Issue number2
StatePublished - Apr 1989

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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