Convergence of iterative methods for elliptic equations with integral boundary conditions

Abstract

In this article, we consider the convergence of iterative method for the system of diference equations, approximating the elliptic two-dimensional equations with variable coe cients and integral boundary conditions. We investigate how convergence of iterative method depends on the structure of spectrum for diference operator with nonlocal conditions. The main goal of the paper is to analyze the influence of the monotonicity of the coefficient in the diferential equation to extension (or reduction) of the region of convergence.