(untitled) (European Journal of Pure and Applied Mathematics, 2013)
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 Î©rÏ†, a special technique of deriving the finite difference scheme in the neighbourhood of the pole pointÂ r = 0 is described. The constructed scheme has the order of approximation Oô°¬(h2r +h2Ï†)/rô°. In theÂ 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.Â