On the numerical solution of a multilevel nonlocal problem

In a rectangular domain, we consider the 5-point approximate solution of the multilevel nonlocal boundary value problem for Laplace’s equation. By constructing the approximate value of the unknown boundary function on the side of the rectangle where the nonlocal condition was given, the solution of the multilevel nonlocal problem is defined as a solution of the Dirichlet problem. The uniform estimation of the error of the approximate solution is of order O(h2), where h is the mesh step. Numerical experiments are presented to support the theoretical analysis made.