On global asymptotic stability of nonlinear higher-order difference equations


Braverman E., KARPUZ B.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.236, no.11, pp.2803-2812, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 236 Issue: 11
  • Publication Date: 2012
  • Doi Number: 10.1016/j.cam.2012.01.015
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2803-2812
  • Keywords: Nonlinear difference equations, Higher-order difference equations, Global asymptotic stability, theta-method, Discretizations of delay equations
  • Dokuz Eylül University Affiliated: No

Abstract

In this paper, we generalize the main theorem of Liz and Ferreiro [E. Liz, J.B. Ferreiro, A note on the global stability of generalized difference equations, Appl. Math. Lett. 15 (2002) 655-6591 and some other global stability results for nonautonomous higher-order difference equations to the case when contraction-type steps are incorporated together with the steps when the difference sequence can increase. The relation to the theta-method for discretization of delay equations is discussed, and some sufficient stability conditions for the numerical scheme are deduced. Several examples are presented to demonstrate sharpness and applications of the results. (C) 2012 Elsevier B.V. All rights reserved.