THE FINITE-DIFFERENCE SCHEME OF HIGHER ORDER OF ACCURACY FOR THE TWO-DIMENSIONAL POISSON EQUATION IN A RECTANGLE WITH REGARD FOR THE EFFECT OF THE DIRICHLET BOUNDARY CONDITION

摘要

Abstracts We investigate the finite-difference scheme of higher order of accuracy on a nine-point template for Poisson’s equation in a rectangle with the Dirichlet boundary condition. We substantiate the error estimate taking into account the influence of the boundary condition. We prove that the accuracy order is higher near the sides of the rectangle than at the inner nodes of the grid set and increase in the approximation order has no impact on the boundary effect.