In this paper, we present a survey of recent results on the Green's functions and on spectrum for stationary problems with nonlocal boundary conditions. Results of Lithuanian mathematicians in the field of differential and numerical problems with nonlocal boundary conditions are described. *The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014).

In this article a stationary problems with general nonlocal boundary conditions is considered. The differential problems and finite difference schemes for solving this problem are investigated. Stability estimates are proved in the maximum norm and the non‐negativity of the solution is investigated. All theoretical results are illustrated by representative examples.

The present paper deals with an alternating direction implicit method for a two dimensional parabolic equation in a rectangle domain with a nonlocal boundary condition in one direction. Sufficient conditions of stability for Peaceman‐Rachford method are established. Results of some numerical experiments are presented.