Well-posedness of a third order of accuracy difference scheme for Bitsadze-Samarskii type multi-point NBVPs

Abstract

A multi-point nonlocal boundary value problem for a multidimensional elliptic equation with Bitsadze-Samarskii condition is considered. A third order of accuracy stable difference scheme for the approximate solution of this problem is presented. The stability, the almost coercive stability and the coercive stability estimates for the solution of this difference scheme are obtained. A numerical analysis is given to justify the theoretical part.