On global asymptotic stability of nonlinear higher-order difference equations

Braverman E., KARPUZ B.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.236, sa.11, ss.2803-2812, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 236 Sayı: 11
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.cam.2012.01.015
  • Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2803-2812
  • Anahtar Kelimeler: Nonlinear difference equations, Higher-order difference equations, Global asymptotic stability, theta-method, Discretizations of delay equations
  • Dokuz Eylül Üniversitesi Adresli: Hayır

Özet

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.