Solution of a two-dimensional elliptic equation with a nonlocal condition

Abstract

A finite-difference method is considered for a two dimensional elliptic equation with a nonlocal condition. The system of difference equations with nonlocal conditions is reduced to two problems for the same system of difference equations with the boundary conditions of the first type. The existence and uniqueness of the solution of the system of difference equations with a nonlocal condition are proven and the error of an approximate solution is estimated.