Existence and uniqueness results for Bitsadze- Samarskii type nonlocal boundary value problem for the semilinear elliptic equation

This paper is deal with the unique solvability of Bitsadze- Samarskii type nonlocal boundary value (NBV) problem for the semi-linear elliptic equation in a Hilbert space. For the approximate solution of this problem, rst and second order of accuracy difference schemes are presented. The convergence estimates for the solutions of these dierence schemes are established. A numerical example illustrating the methods described in this paper is given.