FORM OF THE SOLUTIONS OF DIFFERENCE EQUATIONS VIA LIE SYMMETRY ANALYSIS AND FIBONACCI NUMBERS

被引：0

作者：

Gocen, Melih ^{[1
]}

Folly-Gbetoula, Mensah ^{[2
]}

机构：

[1] Ecevit Univ, Fac Sci, Dept Math, Zonguldak Bulent, Zonguldak, Turkiye

[2] Univ Witwatersrand, Sch Math, ZA-2050 Johannesburg, South Africa

来源：

QUAESTIONES MATHEMATICAE | 2024年 / 47卷 / 02期

关键词：

Difference equation; form of the solutions; reduction; Lie symmetry analysis; Fibonacci numbers; BEHAVIOR; DYNAMICS; SYSTEMS; TERMS;

D O I：

10.2989/16073606.2023.2229520

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：399 / 411

页数：13

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