FORM OF THE SOLUTIONS OF DIFFERENCE EQUATIONS VIA LIE SYMMETRY ANALYSIS AND FIBONACCI NUMBERS
Melih Gocen, Mensah Folly-Gbetoula
article (Uluslararası, Hakemli) | Yazar(lar): Melih Gocen, Mensah Folly-Gbetoula | Yıl: 2024 — Özet: In this paper, we give the form of the solutions of the following rational difference equation
x(n+1) = x(n-3)x(n-1)/a(n)x(n-3)+b(n)x(n-1), (1)
where a(n) and b(n) are sequences of real numbers, by using Lie symmetry
In this paper, we give the form of the solutions of the following rational difference equation
x(n+1) = x(n-3)x(n-1)/a(n)x(n-3)+b(n)x(n-1), (1)
where a(n) and b(n) are sequences of real numbers, by using Lie symmetry analysis and associated with Fibonacci numbers, respectively. We find an interesting relation between the exact solution of Equation (1) and the classical Fibonacci sequence.