Geodesic
Discretization by rational and quasi-rational functions of multi-dimensional elliptic problems in the whole space
Boulmezaoud, T.Z.1 ; Arar, N.2 ; Kerdid, N.3 ; Kourta, A.2
1 Laboratoire de Mathématiques de Versailles, Université de Versailles Saint-Quentin-en-Yvelines 45, avenue des Etats-Unis, 78035, Versailles, cedex, France
2 Department of Mathematics, University Constantine 1, Constantine, Algeria
3 IMSIU, College of Sciences, Department of Mathematics and Statistics, PO-Box 90950, 11623 Riyadh, KSA
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 1, pp. 263-288

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We propose a new spectral method for solving multi-dimensional second order elliptic equations with varying coefficients in the whole space. This method employs an orthogonal family of quasi-rational functions recently discovered by Arar and Boulmezaoud. After proving an error estimate, we present some computational tests which demonstrate the efficiency of the method and the significance of its developmental potential.

DOI : 10.1051/m2an/2015042
Classification : 65N35, 35A01, 35C10, 35C20, 65J99
Keywords: Unbounded domains, spectral methods, rational functions, approximation, the whole space

Boulmezaoud, T.Z. 1 ; Arar, N. 2 ; Kerdid, N. 3 ; Kourta, A. 2

1 Laboratoire de Mathématiques de Versailles, Université de Versailles Saint-Quentin-en-Yvelines 45, avenue des Etats-Unis, 78035, Versailles, cedex, France
2 Department of Mathematics, University Constantine 1, Constantine, Algeria
3 IMSIU, College of Sciences, Department of Mathematics and Statistics, PO-Box 90950, 11623 Riyadh, KSA 
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     title = {Discretization by rational and quasi-rational functions of multi-dimensional elliptic problems in the whole space},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {263--288},
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Boulmezaoud, T.Z.; Arar, N.; Kerdid, N.; Kourta, A. Discretization by rational and quasi-rational functions of multi-dimensional elliptic problems in the whole space. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 1, pp. 263-288. doi: 10.1051/m2an/2015042

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