Geodesic
A generalization of Elsayed's solution to the difference equation $x_{n+1}=\frac{ x_{n-5}}{-1 + x_{n-2}x_{n-5}}$ :
Folly-Gbetoula, Mensah 1   ; Nyirenda, Darlison 1
1 School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 5, p. 613-623 Cet article a éte moissonné depuis la source International Scientific Research Publications

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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.

DOI : 10.22436/jnsa.011.05.03
Classification : 76M60, 39A05, 39A11
Keywords: Difference equation, symmetry, reduction, group invariant

Folly-Gbetoula, Mensah   1   ; Nyirenda, Darlison   1

1 School of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South Africa 
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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 its applications, Tome 11 (2018) no. 5, p. 613-623. doi: 10.22436/jnsa.011.05.03

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