The origin and nature of spurious eigenvalues in the spectral tau method
type: Item
instance of: scholarly article
title: The origin and nature of spurious eigenvalues in the spectral tau method
zbMATH Open document ID: 0924.65077
author: Paul T. Dawkins
author: Steven R. Dunbar
author: Rod W. Douglass
published in: Journal of Computational Physics
publication date: 1999-06-20T00:00:00Z
review text: The tau method, first proposed by Lanczos, is a means of solving boundary value problems for ordinary differential equations using truncated series expansions in a complete set of orthogonal functions. From the author's summary: `The Chebyshev-tau spectral method for approximating eigenvalues of boundary value problems may produce spurious eigenvalues with large positive real parts, even when all true eigenvalues of the problem are known to have negative real parts. We explain the origin and nature of the `spurious eigenvalues' in an example problem. The explanation will demonstrate that the large positive eigenvalues are an approximation of infinite eigenvalues in a nearby generalized eigenvalue problem'.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34L15
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 1282757
zbMATH Keywords: Lanczos tau method
zbMATH Keywords: series expansions
zbMATH Keywords: orthogonal functions
zbMATH Keywords: Chebyshev-tau spectral method
zbMATH Keywords: spurious eigenvalues
zbMATH Keywords: generalized eigenvalue problem
reviewed by: Waldemar Velte
MaRDI profile type: Publication
full work available at URL: jcph.1998.6095
OpenAlex ID: W2010799088
cites work: Complex coordinate methods for hydrodynamic instabilities and Sturm- Liouville eigenproblems with an interior singularity
cites work: Q3993205
cites work: Q3727595
cites work: Chebyshev Methods for Ordinary Differential Equations
cites work: Q5533821
cites work: A modified tau spectral method that eliminates spurious eigenvalues
cites work: Q4275389
cites work: The pseudospectral method for solving differential eigenvalue problems
cites work: Trigonometric Interpolation of Empirical and Analytical Functions
cites work: Q3846497
cites work: Elimination of spurious eigenvalues in the Chebyshev tau spectral method
cites work: Accurate solution of the Orr–Sommerfeld stability equation
cites work: The Tau Method
cites work: Some remarks on multivariate Chebyshev polynomials
cites work: Two very accurate and efficient methods for computing eigenvalues and eigenfunctions in porous convection problems
cites work: Numerical solution of eigenvalue problems using spectral techniques
cites work: A Chebyshev method for the solution of boundary value problems
cites work: Removal of spurious modes encountered in solving stability problems by spectral methods
DOI: 10.1006/JCPH.1998.6095
description: scientific article; zbMATH DE number 1282757