A modified tau spectral method that eliminates spurious eigenvalues

David R. Gardner, Steven A. Trogdon, Rod W. Douglass

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Abstract

A modified tau spectral method is presented which eliminates the spurious eigenvalues produced by the usual tau method. The modified tau method essentially involves an appropriate factorization of the differential operators in the eigenvalue problem. It is developed for eigenvalue problems posed as single differential equations or as systems of such equations. Several eigenvalue problems are solved using both the usual and modified Chebyshev-tau methods, including the Orr-Sommerfeld stability equation for plane Poiseuille flow. The convergence of the modified tau method is shown to be at least as rapid as that of the usual tau method. The use of the tau coefficients in indicating convergence is also discussed.

Original languageEnglish (US)
Pages (from-to)137-167
Number of pages31
JournalJournal of Computational Physics
Volume80
Issue number1
DOIs
StatePublished - Jan 1989

Bibliographical note

Funding Information:
This work was supported by the Mechanical Engineering Department of the University of Nebraska-Lincoln and by the National ScienceF oundationt hroughG rant CBT-8612427T. his support is gratefullya cknowledged.

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