Stability under constantly acting perturbations for difference equations and averaging

TL;DR

This paper investigates the stability of solutions to difference equations and their averaged counterparts under continuous perturbations, providing theoretical assertions based on a key stability theorem.

Contribution

It introduces new theoretical results on the stability of difference equations under persistent perturbations, linking exact and averaged solutions.

Findings

Established conditions for solution closeness over infinite intervals

Derived stability assertions from a fundamental theorem

Enhanced understanding of perturbation effects on difference equations

Abstract

We consider the problem of closeness of solutions of an exact and an averaged difference equations on an infinite interval. Appropriate assertions are derived from one special theorem on the stability under constantly acting perturbations.