On a system of difference equations of third order solved in closed form

Main Article Content

Youssouf AKROUR
https://orcid.org/0000-0003-3660-7317
Nouressadat Touafek
https://orcid.org/0000-0001-7079-6794
Yacine Halim
https://orcid.org/0000-0001-7582-8257

Abstract

In this work, we show that the system of difference equations
xn+1=(ayn-2xn-1yn+bxn-1yn-2+cyn-2+d)/(yn-2xn-1yn),
yn+1=(axn-2yn-1xn+byn-1xn-2+cxn-2+d)/(xn-2yn-1xn),
where n belongs to the set of positive integer numbers, x-2, x-1, x0, y-2, y-1 and y0 are arbitrary nonzero real numbers, and the parameters a, b, c and d are arbitrary real numbers with d nonzero can be solved in a closed form.
We will see that when a = b = c = d = 1, the solutions are expressed using the famous Tetranacci numbers. In particular, the results obtained here extend those in our recent work.

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How to Cite
[1]
AKROUR, Y., Touafek, N. and Halim, Y. 2021. On a system of difference equations of third order solved in closed form. Journal of Innovative Applied Mathematics and Computational Sciences. 1, 1 (Dec. 2021), 1–15.
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Research Articles

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