A modified chebyshev pseudospectral method with an O(n−1) time step restriction

Dan Kosloff, Hillel Tal-Ezer

Research output: Contribution to journalArticlepeer-review

Abstract

The extreme eigenvalues of the Chebyshev pseudospectral differentiation operator are O(N2), where N is the number of grid points. As a result of this, the allowable time step in an explicit time marching algorithm is O(N−2) which, in many cases, is much below the time step dictated by the physics of the PDE. In this paper we introduce a new differentiation operator whose eigenvalues are O (N) and the allowable time step is O (N−1). The new algorithm is based on interpolating at the zeroes of a parameter dependent, nonperiodic trigonometric function. The properties of the new algorithm are similar to those of the Fourier method but in addition it provides highly accurate solution for nonperiodic boundary value problems.

Original languageEnglish
Pages (from-to)457-469
Number of pages13
JournalJournal of Computational Physics
Volume104
Issue number2
DOIs
StatePublished - Feb 1993

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