A modified Chebyshev-tau method for a hydrodynamic stability problem

Abstract

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Authors

C.I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

I. S. Pop
Babes-Bolyai University, Faculty of Mathematics and Informatics

Keywords

Chebyshev spectral method, differential eigenvalue problem, hydrodynamic stability

Cite this paper as:

C.I. Gheorghiu, I.S. Pop, A modified Chebyshev-tau method for a hydrodynamic stability problem, Proceedings of ICAOR (International Conference on Approximation, Optimization – Romania), 1996, vol. II, pp. 119-126.

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Journal

Proceedings of the International Conference on Approximation and Optimization (Romania) – ICAOR

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DOI
Print ISSN

0169-3913

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References

1. Ch. Cabos, A preconditioning of the tau operator for ordinary differential equations, ZAMM 74 (1994), 521–532.

2. C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zhang, Spectral methods in fluid dynamics, Springer-Verlang, New York/Berlin (1998).

3. W. Heinrichs, A stabilized treatment of the biharmonic operator with spectral methods, SIAM J. Sci. Stat.Comput. 12 (1991), 1162-1172.

4. M. Heigemann, Chebyshev matrix operator method for the solution of integrated forms of linear ordinary differential equations, Acta Mech. (to appear).

5. W. Huang and D. M. Sloan, The pseudospectral method for solving differential eigenvalue problems, J. Comput.Phys. 111 (1994), 399–409.

6. K. A. Lindsay and R. R. Ogden, A practical implementation of spectral methods resistant to the generation of spurious eigenvalues, Intl. J. Numer. Meth. Fluids 15 (1992), 1277–1294.

7. K. M. Liu and E. L. Ortiz, Tau method approximation of differential eigenvalue problems where the spectral parameter enters nonlineary, J. Comput. Phys. 72 (1987), 299–310.

8. S. A. Orszag, Accurate solution of the Orr-Sommerfeld stability equation, J. Fluid Mech. 50 (1971), 689–703.

9. J. Shen, Efficient spectral-Galerkin method II. Direct solvers of second and fourth order equations by using Chebyshev polynomials, SIAM J. Sci. Stat. Comput. 16 (1995), 74–8

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