A solvable system of nonlinear difference equations
Authors : Abdullah Şahinkaya, Ibrahim Yalçinkaya, Durhasan Turgut Tollu
Pages : 10-20
View : 15 | Download : 4
Publication Date : 2020-07-30
Article Type : Research
Abstract :In this paper, we show that the following systems of nonlinear difference equations x_{n+1}=((x_{n}y_{n}+a)/(x_{n}+y_{n})),y_{n+1}=((y_{n}z_{n}+a)/(y_{n}+z_{n})),z_{n+1}=((z_{n}x_{n}+a)/(z_{n}+x_{n})) for n∈ℕ₀ where a∈[0,∞) and the initial values x₀, y₀, z₀ are real numbers, can be solved in explicit form. Also, we investigate the asymptotic behavior of the solutions by using these formulae and give some numerical examples which verify our theoretical result.Keywords : Asymptotic behavior, explicit solution, nonlinear difference equation, system