Asymptotic approximations for second-order linear difference equations in Banach algebras, I ✩

An asymptotic approximation theory is developed for some classes of linear second-order difference equations in Banach algebras, subject to “finite moments perturbations.” The special case of linear matrix difference equations (or, equivalently, of second-order systems) is included. Rigorous and explicitly computable bounds for the error terms are obtained. © 2007 Elsevier Inc. All rights reserved