Paper title:

Two-dimensional Spectral Approximation

Published in: Issue 2, (Vol. 11) / 2017
Publishing date: 2017-10-13
Pages: 21-25
Author(s): ISMAHENE Sehili, ZERROUG Abdelhamid
Abstract. In this article, we propose a two-dimensional polynomial basis which extends Legendre series approximation to bivariate functions. We also present a theoretical study of the stability and the error estimation of the Tau spectral method in the constructed basis
Keywords: Two-dimensional Basis, Rodrigues Construction, Error Estimation, Stability

1. A. Quarteroni, C. Canuto, M. Y. Hussaini, T. A. Zang, Spectral Methods Fundamentals in Single Domains, Springer 2006.

2. Alvise Sommariva, Marco Vianello and Renato Zanovello. Adaptive bivariate Chebyshev

3. approximation, Department of Pure and Applied Mathematics University of Padovavia Belzoni 7, 35131 - Padova (Italy).

4. C. Canuto, M. Yousuff Hussaini, Alfio Quarteroni, & Thomas A. Zang, Spectral Methods in Fluid Dynamics. Springer Series in Computational Physics. Springer, 1987.

5. K. Smyth Gordon, Polynomial Approximation, Department of Mathematics, University of Queensland, May 1997.

6. Smyth, G. K. Polynomial approximation, Encyclopedia of Biostatistics, 1998.

7. Rafael C. Gonzalez et Richard E. Woods, Digital Image Processing, Pearson Prentice Hall.

8. Stone, M, The Generalized Weierstrass Approximation Theorem, Mathematics Magazine, 1948.

9. Robin A. Driscoll, Nicholas Hale, and Lloyd N. Trefethen, Chebfun Guide.

10. T. J. Rivlin, An Introduction to the Approximation of Functions, Dover, New York, 1981.

11. Z. Battles and L.N. Trefethen, An extension of Matlab to continuous functions and operators, 2003, submitted to SIAM J. Sci. Comp. (preprint available online, Computing Laboratory, Oxford University).

Back to the journal content
Creative Commons License
This article is licensed under a
Creative Commons Attribution-ShareAlike 4.0 International License.
Home | Editorial Board | Author info | Archive | Contact
Copyright JACSM 2007-2023