Method of corrections by higher order differences for Poisson equation with nonlocal boundary conditions

We consider the Bitsadze–Samarskii type nonlocal boundary value problem for Poisson equation in a unit square, which is solved by a difference scheme of second-order accuracy. Using this approximate solution, we correct the right-hand side of the difference scheme. It is shown that the solution of the corrected scheme converges at the rate O(|h|s)O(|h|s) in the discrete L2L2-norm provided that the solution of the original problem belongs to the Sobolev space with exponent s∈[2,4]s∈[2,4].