Asian Journal of Mathematics and Computer Research
 

Asian Journal of Mathematics and Computer Research, ISSN No. : 2395-4205 (Print), 2395-4213 (Online), Vol.: 18, Issue.: 3

Original Research Article

CREATION OF TWO-DIMENSIONAL LEGENDRE BASIS AND SOME PROPERTIES

 

ISMAHENE SEHILI1*,  ABDELHAMID ZERROUG1 AND AZEDINE RAHMOUNE2
1Department of Mathematics, Faculty of Exacte Sciences, University of Biskra, Algeria.
2Department of Mathematics, University of Borj Bouariridj, Algeria.

Abstracts

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.