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A practical implementation of spectral methods resistant to the generation of spurious eigenvalues

โœ Scribed by K. A. Lindsay; R. R. Ogden

Book ID
102843818
Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
941 KB
Volume
15
Category
Article
ISSN
0271-2091

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โœฆ Synopsis

This work describes a practical way of constructing a spectral representation of linear boundary value problems (BVPs) using a tau method. All BVPs are treated as first-order systems, unlike most implementations which tend to view the problem in terms of a single high-order differential equation. For most applications this formulation will adhere more closely to the natural derivation of the original equations from, for example, a series of conservation laws. The technique is exemplified for Chebyshev polynomials in a variety of real applications, although detailed results are provided for any polynomial basis.

๐Ÿ“œ SIMILAR VOLUMES

The Origin and Nature of Spurious Eigenv
The Origin and Nature of Spurious Eigenvalues in the Spectral Tau Method
โœ Paul T. Dawkins; Steven R. Dunbar; Rod W. Douglass ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 226 KB

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 eigenvalu