Ulam - Hyers Stability of Second Order Difference Equations using Laplace Transforms

Abstract

This article explores the Ulam-Hyers stability of both homogeneous and non-homogeneous second-order difference equations, which are widely applied in control systems and digital signal processing. Using the Laplace transform, we analyze the convergence of these newly defined difference equations. Additionally, we extend our study to the Ulam-Hyers stability of discrete values (difference equations) within an open subinterval by providing a detailed analysis of their properties through Laplace transformation. To enrich our theoretical findings, numerical examples are stated and these examples demonstrates and extend the applications of our theory.