Analysis of linear difference equations with variable coefficients

Abstract

In this paper, we studies the explicit solution of a linear difference equation of unbounded order with variable coefficients is presented. The solutions of nonhomogeneous and homogeneous linear difference equations of order N with variable coefficients are obtained. From these solutions, we also get expressions for the product of companion matrices, and the power of a companion matrix. This paper presents explicit solutions in terms of coefficients of linear difference equations with variable coefficients, for both the unbounded order case and the Nth-order case.