arXiv:0910.5088 Abstract | arXiv Analytics

arXiv:0910.5088 [math.NA]Abstract References Reviews Resources

A spectral method based on $(0,2)$ Jacobi polynomials. Application to Poisson problems in a sphere

Published 2009-10-27Version 1

A new spectral method is built resorting to $(0,2)$ Jacobi polynomials. We describe the origin and the properties of these polynomials. This choice of polynomials is motivated by their orthogonality properties with the respect to the weight $r^2$ used in spherical geometry. New results about Jacobi-Gauss-Lobatto quadratures are proven, leading to a discrete Jacobi transform. Numerical tests for Poisson problems in a sphere are presented using the C++ library \textsc{lorene}.

Comments: 30 pages, 5 figures

Categories: math.NA, gr-qc

Subjects: 65N35

Keywords: jacobi polynomials, spectral method, poisson problems, application, discrete jacobi transform

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