Journal of Innovative Applied Mathematics and Computational Sciences
Volume 1, Numéro 1, Pages 1-15
2021-12-30

On A System Of Difference Equations Of Third Order Solved In Closed Form

Authors : Akrour Youssouf .

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.

Keywords

System of difference equations, general solution, Tetranacci numbers.