A solvable system of nonlinear difference equations

Yıl 2020, Cilt: 2 Sayı: 1, 10 - 20, 30.07.2020

Abdullah Şahinkaya İbrahim Yalçınkaya Durhasan Turgut Tollu

Öz

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.

Anahtar Kelimeler

Asymptotic behavior, explicit solution, nonlinear difference equation, system

Kaynakça

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