Advances in Difference Equations 
Volume 2004 (2004), Issue 2, Pages 121-139
doi:10.1155/S168718390430806X

Rate of convergence of solutions of rational difference equation of second order

S. Kalabušić and M. R. S. Kulenović

 Department of Mathematics, University of Rhode Island, Kingston 02881-0816, RI, USA
Received 13 August 2003; Revised 7 October 2003

Abstract

We investigate the rate of convergence of solutions of some special cases of the equation xn+1=(α+βxn+γxn−1)/(A+Bxn+Cxn−1), n=0,1,…, with positive parameters and nonnegative initial conditions. We give precise results about the rate of convergence of the solutions that converge to the equilibrium or period-two solution by using Poincaré's theorem and an improvement of Perron's theorem.