DISCRETIZATION BY RATIONAL AND QUASI-RATIONAL FUNCTIONS OF MULTI-DIMENSIONAL ELLIPTIC PROBLEMS IN THE WHOLE SPACE

摘要

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.