A highly accurate corrected scheme in solving the Laplace's equation on a rectangle

A pointwise error estimation of the form 0(ρh8),h is the mesh size, for the approximate solution of the Dirichlet problem for Laplace's equation on a rectangular domain is obtained as a result of three stage (9-point, 5-point and 5-point) finite difference method; here ρ = ρ(x,y) is the distance from the current grid point (x,y,) ε Πh to the boundary of the rectangle Π