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A practical implementation of spectral methods resistant to the generation of spurious eigenvalues
Author(s) -
Lindsay K. A.,
Ogden R. R.
Publication year - 1992
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650151104
Subject(s) - spurious relationship , mathematics , chebyshev filter , eigenvalues and eigenvectors , boundary value problem , spectral method , chebyshev polynomials , polynomial , representation (politics) , basis (linear algebra) , calculus (dental) , algebra over a field , mathematical analysis , pure mathematics , geometry , medicine , dentistry , quantum mechanics , politics , political science , statistics , physics , law
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.