Bounds for the solutions of second-order linear difference equations

Abstract

Simple bounds are established for the solutions of second-order homogeneous linear difference equations in ranges in which the solutions are exponen ti al in character. The results are applied to a recent algorithm for the computation of subdominant solutions of second-order linear difference equation s, homoge neous or otherwise. Strict and extremely realistic bounds are obtained for the truncation error associated with the algorithm in a number of examples, including AngerWeber functions, Struve functions , and the solution of a differential equation in Chebyshev series.