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arXiv · 1902.06518

On certain sixth order difference equations

D. Nyirenda·M. Folly-Gbetoula
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Abstract

We use the Lie group analysis method to investigate the invariance properties and the solutions of \begin{align*} x_{n+1} =\frac{x_{n-5}x_{n-3}}{x_{n-1}(a_n +b_nx_{n-5}x_{n-3})}. \end{align*} We show that this equation has a two-dimensional Lie algebra and that its solutions can be presented in a unified manner. Besides presenting solutions of the recursive sequence above where $(a_n)$ and $(b_n)$ are sequences of real numbers, some specific cases are emphasized.

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D. Nyirenda, M. Folly-Gbetoula. 2019-02-18. On certain sixth order difference equations. https://arxiv.org/abs/1902.06518

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