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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

MSC:
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
Software:
EISPACK
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References:
[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
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