Approximation of solutions to nonautonomous difference equations

Abstract

We study the asymptotic properties of solutions to nonautonomous dierence equations
of the form

\delta^m x_n  = 

a_n f ( n,  x_{\sima(n)} ) + b_n,

\quad 

f :\mathbb{N} \times \mathbb{R} \to \mathbb{R} ,

\quad

\sigma \mathbb{N} \to \mathbb{N}.

Using the iterated remainder operator and asymptotic dierence pairs we establish some results concerning approximative solutions and approximations of solutions. Our approach
allows us to control the degree of approximation.