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

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 aweighted integral boundary condition in one coordinate direction. We consider the alternatingdirection method for a system of difference equations that approximates Poisson equationwith weighed integral boundary conditions with the fourth-order accuracy. Sufficient conditionsof stability for ADI method are investigated numerically. An analysis of results ofcomputational experiments is presented.