zbMATH — the first resource for mathematics

Elimination of spurious eigenvalues in the Chebyshev tau spectral method. (English) Zbl 0717.65063
The authors present a simple modification of the Chebyshev tau method which avoids spurious eigenvalues, and apply it to finding the eigenvalues of the Orr-Sommerfeld equation.
Reviewer: J.D.P.Donnelly

65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
Full Text: DOI
[1] Orszag, S.A., J. fluid mech., 50, 689, (1971)
[2] Gottlieb, D.; Orszag, S.A., Numerical analysis of spectral methods: theory and applications, () · Zbl 0561.76076
[3] Gary, J.; Helgason, R., J. comput. phys., 5, 169, (1970)
[4] Zebib, A., J. comput. phys., 53, 443, (1984)
[5] Brenier, B.; Roux, B.; Bontoux, P., J. theor. appl. mech., 5, 95, (1986)
[6] Zebib, A., J. comput. phys., 70, 521, (1987)
[7] Gardner, D.R.; Trogdon, S.A.; Douglass, R.W., J. comput. phys., 80, 137, (1989)
[8] Garbow, B.S.; Boyle, J.M.; Dongarra, J.J.; Moler, C.B., Matrix eigensystem routine-EISPACK guide extension, (1977), Springer-Verlag New York · Zbl 0368.65020
[9] Moler, C.B.; Stewart, G.W., SIAM J. numer. anal., 10, 241, (1973)
[10] Stewart, G.W., (), 193
[11] Delves, L.M.; Mohamed, J.L., Computational methods for integral equations, (), 212 · Zbl 0592.65093
[12] Drazin, P.G.; Reid, W., Hydrodynamic stability, (1981), Cambridge Univ. Press New York · Zbl 0449.76027
[13] Aird, T.J., The IMSL library, (), 264
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.