zbMATH — the first resource for mathematics

Rate of convergence of solutions of rational difference equation of second order. (English) Zbl 1079.39007
The authors give precise results about the rate of convergence of the solutions of the rational difference equations $x_{n+1}=\frac{B}{x_n}+\frac{C}{x_{n-1}},\quad n=0,1,2,...$
$x_{n+1}=\frac{p+x_n+x_{n-1}}{qx_n+x_{n-1}},\quad n=0,1,2,...$
$x_{n+1}=\frac{p+x_n+x_{n-1}}{q+x_{n-1}},\quad n=0,1,2,...$ that converge to the equilibrium or period-two solution. The main idea in their approach is to linearize the difference equation under study about the attracting equilibrium or period-two solution, and then use Poincaré are theorem and/or an improvement of Perron’s theorem due to M. Pituk [J. Difference Equ. Appl. 8, No.3, 201–216 (2002; Zbl 1002.39014)].

MSC:
 39A11 Stability of difference equations (MSC2000) 39A20 Multiplicative and other generalized difference equations
Full Text: