A Chebyshev-Galerkin method for fourth order problems

Abstract

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Authors

I. S. Pop
Babeș-Bolyai University, Faculty of Mathematics and Informatics
C.I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis

Keywords

Chebyshev-Galerkin spectral method; differential eigenvalue problem

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Paper coordinates

I.S. Pop, C.I. Gheorghiu, A Chebyshev-Galerkin method for fourth order problems, Proceedings of ICAOR (International Conference on Approximation, Optimization – Romania), Cluj-Napoca, July-August 1996, vol. II, pp. 217-220.

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Approximation and Optimization

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References

[1]  C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A., Zhang,  Spectral methods in fluid dynamics,  Springer-Verlag, New York/Berlin, 1988.

[2] D. Funaro and W. Heinrichs,  Some results about the pseudospectral approximation of one-dimensional fourt-order problems.  Numer. Math. 58, 1990, 1399-418.

[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] S. A. Orszag,  Accurate solution of the Orr-Sommerfeld stability equations,  J. Fluid Mech. 50, 1971, 689-703.

[7] 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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