On the Chebyshev-tau approximation for some singularly perturbed two point boundary value problems – Numerical experiments

Abstract

In this paper we are concerned with numerical stability of Chebyshev-tau method in solving some singularly perturbed two-point boundary value problems.

We consider linear as well as nonlinear (convection-dominated flow) problems. In order to avoid the lack of numerical stability of this method we try a smoothing technique as well as a domain decomposition for linear problems.

Some successful numerical experiments are carried out.

Authors

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

Keywords

Chebyshev-tau; stability; two-point boundary value problem; singularly perturbed; steady state Burger; smoothing;

References

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Cite this paper as

C. I. Gheorghiu, S.I. Pop, On the Chebyshev-tau approximation for some singularly perturbed two point boundary value problems – Numerical experiments, Rev. Anal. Numér. Théor. Approx. 24 (1995) 117-124.

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Journal

Rev. Anal. Numér. Théor. Approx.

Publisher Name

Editions de l’Academie Roumaine

Print ISSN

1222-9024

Online ISSN

2457-8126

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References

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[2] C. I. Gheorghiu, On a Linear Singularity Perturbed TPBVP, Univ. of Cluj-Napoca, Seminar of Functional Analysis and Numerical Methods, Preprint 1 (1988), pp. 67-74.

[3] D. Gottlieb, S.A. Orszag, Numerical analysis of Spectral Methods: Theory and Applications, SIAM Philadelphia, 1977.

[4] C. Johson, Numerical solutions of p.d.e. by the f.e.m., Cambridge Univ. Press. 1987.

[5] R. B. Kellog, A. Tsan, analysis of some difference approximations for a singular perturbaiton problem without turning points, Math. Comput. 32, pp. 1025-1039 (1978).

[6] Y. Maday, A. Quarteroni, Legendre and Chebyshev Spectral Approixmation of Burgers’ Equation, Numer. Math. 37, pp. 321-332 (1981).

[7] S.A. Orszag, Accurate Solution of the Orr-Sommerfeld stability equation, J. Fluid Mech., 50, pp. 689-703 (1971).

[8] M. Stynes, E. O’Riordan, An analysis of a t.p.b.c.p. with a boundary layer, using only finite element techniques, Univ. College Cork. Ireland, 1989.

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