On the equivalence of discrete Sturm–Liouville problem with nonlocal boundary conditions to the algebraic eigenvalue problem

Abstract

We consider the finite difference approximation of the second order Sturm–Liouville equation with nonlocal boundary conditions (NBC). We investigate the condition when the discrete Sturm–Liouville problem can be transformed to an algebraic eigenvalue problem and denote this condition as solvability condition. The examples of the solvability for the most popular NBCs are provided.
 The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/ 2014).