Generalized finite difference method for solving two-interval Sturm-Liouville problems with jump conditions

Abstract

We consider a Sturm-Liouville problem defined on two disjoint intervals together with additional jump conditions across the common endpoint of these intervals. Based on Finite Difference Method (FDM) we have developed a new tecnique for solving such type nonstandard boundary value problems (BVP). To show applicability and effectiveness of the proposed generalization of FDM, we solved a simple but illustrative example. The obtained numerical solutions are graphically compared with the corresponding exact solutions.