Sturm-Liouville Difference Equations Having Special Potentials

TL;DR

This paper introduces a novel approach to solving Sturm-Liouville difference equations with special potentials, providing solution representations, asymptotic formulas, and numerical eigenfunction comparisons to enhance spectral theory applications.

Contribution

It offers new methods for analyzing Sturm-Liouville difference equations with specific potentials, including solution representations and asymptotic analysis.

Findings

Derived solution representations and asymptotic formulas.

Numerical comparisons of eigenfunctions.

Applications demonstrating spectral theory relevance.

Abstract

In this paper, we present a new approachment for Sturm-Liouville problem having special potentials. We acquire the representations of solutions and asymptotic formulas for solutions with regard to initial conditions. Also, a few applications are given to show the requirement of Sturm-Liouville difference equations having potential function in view of suitability to the spectral theory. The approximate numerical outcomes for the eigenfunctions are compared with each other.