A generalization of Elsayed's solution to the difference equation \(x_{n+1}=\frac{ x_{n-5}}{-1 + x_{n-2}x_{n-5}}\)

Volume 11, Issue 5, pp 613--623 http://dx.doi.org/10.22436/jnsa.011.05.03
Publication Date: March 28, 2018 Submission Date: July 20, 2017 Revision Date: September 26, 2017 Accteptance Date: March 01, 2018

Authors

Mensah Folly-Gbetoula - School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa. Darlison Nyirenda - School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa.


Abstract

In this paper, we obtain solutions to difference equations of the form \[ x_{n+1}=\frac{ x_{n-5}}{a_n+b_n x_{n-2}x_{n-5}},\] where \((a_{n})\) and \((b_{n})\) are sequences of real numbers. Consequently, a result of Elsayed is generalized. To achieve this, we use Lie symmetry analysis.


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ISRP Style

Mensah Folly-Gbetoula, Darlison Nyirenda, A generalization of Elsayed's solution to the difference equation \(x_{n+1}=\frac{ x_{n-5}}{-1 + x_{n-2}x_{n-5}}\), Journal of Nonlinear Sciences and Applications, 11 (2018), no. 5, 613--623

AMA Style

Folly-Gbetoula Mensah, Nyirenda Darlison, A generalization of Elsayed's solution to the difference equation \(x_{n+1}=\frac{ x_{n-5}}{-1 + x_{n-2}x_{n-5}}\). J. Nonlinear Sci. Appl. (2018); 11(5):613--623

Chicago/Turabian Style

Folly-Gbetoula, Mensah, Nyirenda, Darlison. "A generalization of Elsayed's solution to the difference equation \(x_{n+1}=\frac{ x_{n-5}}{-1 + x_{n-2}x_{n-5}}\)." Journal of Nonlinear Sciences and Applications, 11, no. 5 (2018): 613--623


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