On the matrix form of second-order linear difference equations

TL;DR

This paper explores transforming second-order linear difference equations into first-order systems by splitting the unknown function into two auxiliary functions, offering a potentially useful approach for solving physical problems.

Contribution

It introduces a novel method of splitting the unknown grid function into two auxiliary functions for transforming difference equations.

Findings

The approach can be applied to various physical problems.

It provides an alternative to previous transformation methods.

Examples demonstrate the effectiveness of the proposed method.

Abstract

Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new auxiliary functions, which have definite properties. Several examples show that proposed approach can be useful in solving different physical problems.