A group theory approach towards some higher order difference equations, solutions, periodicity and asymptotic behavior

Abstract

In this paper, we apply a group theory method to derive the generators of the Lie algebra for a class of (k+1)th order dierence equations. We then nd solutions to the dierence equations and study periodicity by giving sucient conditions for existence of certain periodicities. We further look at the asymptotic behaviour of solutions satisfying certain properties. Our results generalise some known results in the literature.

Key words: Dierence equation, symmetry, reduction, group invariant solutions.