Comparative Analysis of the Modified SOR and BGC Methods Applied to the Poleness Conservative Finite Difference Scheme

Arzu Erdem

Abstract

The poleness conservative finite difference scheme based on the weak solution of Poisson equation in polar coordinates is studied. Due to the singularity at r = 0 in the considered polar domain Ωrφ, a special technique of deriving the finite difference scheme in the neighbourhood of the pole point r = 0 is described. The constructed scheme has the order of approximation O􏰬(h2r +h2φ)/r􏰭. In the second part of the paper the structure of the corresponding non-symmetric sparse block matrix is analyzed. A special algorithm based on SOR-method is presented for the numerical solution of the corresponding system of linear algebraic equations. The theoretical result are illustrated by numerical examples for continuous as well as discontinuous source function. 

Keywords

Finite difference method, elliptic problem, polar coordinates, sparse matrix

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