## 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

**Gheorghiu**

Tiberiu Popoviciu Institute of Numerical Analysis

**Pop**

Babeș-Bolyai University, Faculty of Mathematics

## Keywords

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

### References

See the expanding block below.

## 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.

## About this paper

##### Journal

Rev. Anal. Numér. Théor. Approx.

##### Publisher Name

Editions de l’Academie Roumaine

##### Paper on journal website

##### Print ISSN

1222-9024

##### Online ISSN

2457-8126

##### MR

?

##### ZBL

?

## Google Scholar

?

[1] C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A., Zang, *Spectral Methods in Fluid Dynamics*, Springer-Verlag, Springer Series in Computational Physics, 1988.

[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.