On the solution of a nonlocal problem

In a rectangular domain, we consider the Bitsadze–Samarskii nonlocal boundary value problem for the two-dimensional Poisson equation. The solution of this problem is defined as a solution of the local Dirichlet boundary value problem, by constructing a special method to find a function as the boundary value on the side of the rectangle, where the nonlocal condition was given. Further, the five point approximation of the Laplace operator is used for the realization of the proposed method. Numerical experiments are illustrated in the last section to support the analysis made.