WITHDRAWN: Method of corrections by higher order differences for one nonlocal boundary-value problem

Abstract

Abstract 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 ) in the discrete L 2 -norm provided that the solution of the original problem belongs to the Sobolev space with exponent s ∈ [ 2 , 4 ] .