M-matrices and one-dimensional discrete Sturm–Liouville problems with nonlocal boundary conditions

Abstract

This article is the second part of a survey dedicated to M-matrices and the application of the finite difference method to elliptic problems with nonlocal boundary conditions. Here, we examine cases in which the matrix of the resulting system of linear equations is an M-matrix. Here, we address the discrete Sturm–Liouville problem with nonlocal boundary conditions, describing its spectrum in one-dimensional case. This enables us to determine the values of the nonlocality parameters for which the finite difference scheme is represented by an M-matrix.