Operational Method for Finite Difference Equations

TL;DR

This paper introduces a fast, direct operational method for solving linear finite difference equations with constant coefficients, utilizing polynomial translation operators to efficiently find particular solutions.

Contribution

It presents a novel operational approach based on polynomial translation operators, expanding the toolkit for solving finite difference equations.

Findings

Develops a polynomial-based translation operator method

Enables efficient computation of particular solutions

Suggests potential for expanding operational methods

Abstract

In this article I present a fast and direct method for solving several types of linear finite difference equations (FDE) with constant coefficients. The method is based on a polynomial form of the translation operator and its inverse, and can be used to find the particular solution of the FDE. This work raises the possibility of developing new ways to expand the scope of the operational methods.