CREATION OF TWO-DIMENSIONAL LEGENDRE BASIS AND SOME PROPERTIES

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Published: 2017-06-13

Page: 134-142


ISMAHENE SEHILI *

Department of Mathematics, Faculty of Exacte Sciences, University of Biskra, Algeria.

ABDELHAMID ZERROUG

Department of Mathematics, Faculty of Exacte Sciences, University of Biskra, Algeria.

AZEDINE RAHMOUNE

Department of Mathematics, University of Borj Bouariridj, Algeria.

*Author to whom correspondence should be addressed.


Abstract

In this paper, we introduce a new bi-dimensional polynomial basis for approximating bivariate functions. We start this construction by searching the eigenvalues of the Legendre differential equation in 2D, then this basis was constructed using a Rodrigues formula. Efficient numerical results are obtained by the approximation of some bivariate functions in this basis, and compared by the least squares method with the Chebychev polynomials.

Keywords: Two-dimensional legendre basis, Rodrigues formula, Approximation in 2D, Bi-spectral method


How to Cite

SEHILI, I., ZERROUG, A., & RAHMOUNE, A. (2017). CREATION OF TWO-DIMENSIONAL LEGENDRE BASIS AND SOME PROPERTIES. Asian Journal of Mathematics and Computer Research, 18(3), 134–142. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/1051

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