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The present paper deals with a generalization of the alternating-direction implicit (ADI) method for a two dimensional Poisson equation in a rectangle domain with a weighted integral boundary condition in one coordinate direction. We consider the alternating direction method for a system of difference equations that approximates Poisson equation with weighed integral boundary conditions with the fourth-order accuracy. Sufficient conditions of stability for ADI method are investigated numerically. An analysis of results of computational experiments is presented.

Numerical investigation of alternating-direction method for Poisson equation with weighted integral conditions