Volume 50, Number 1, January-February 2016
|Page(s)||263 - 288|
|Published online||28 January 2016|
Discretization by rational and quasi-rational functions of multi-dimensional elliptic problems in the whole space
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
Revised: 4 March 2015
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.
Mathematics Subject Classification: 65N35 / 35A01 / 35C10 / 35C20 / 65J99
Key words: Unbounded domains / spectral methods / rational functions / approximation / the whole space
© EDP Sciences, SMAI, 2016
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