Symmetries, Reductions and Exact Solutions of a Class of (2<i>k</i> + 2)th-Order Difference Equations with Variable Coefficients

Abstract

We perform a Lie analysis of (2k+2)th-order difference equations and obtain k+1 non-trivial symmetries. We utilize these symmetries to obtain their exact solutions. Sufficient conditions for convergence of solutions are provided for some specific cases. We exemplify our theoretical analysis with some numerical examples. The results in this paper extend to some work in the recent literature.

Keywords

• difference equation
• group invariant solutions
• periodicity
• reduction
• symmetry