Discretization by rational and quasi-rational functions of multi-dimensional elliptic problems in the whole space

Boulmezaoud, T.Z.; Arar, N.; Kerdid, N.; Kourta, A.

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 1, pp. 263-288.

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.

Classification : 65N35, 35A01, 35C10, 35C20, 65J99
Mots clés : Unbounded domains, spectral methods, rational functions, approximation, the whole space

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