Accommodation of zero-valued characteristic roots in the classical solution expression for linear, homogeneous, constant-coefficient difference equations

Abstract

Linear, constant-coefficient difference equations play a central role in many areas of engineering, where cases involving repeated zero-valued characteristic roots are sometimes of particular interest. Unfortunately, the classical solution expression presented in the mathematical literature of difference equations is not valid for this latter case. In this paper we develop a unique generalization of the classical solution expression for linear, constant-coefficient, homogeneous difference equations that accommodates the most general case of repeated zero-valued characteristic roots, thereby “completing” the classical theory. A worked example is presented to illustrate our result.