General solutions to systems of difference equations and some of their representations

Khelifa, Amira; Halim, Yacine

doi:10.1007/s12190-020-01476-8

Cited by 8 publications

(2 citation statements)

References 24 publications

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“…Recently, there has been a growing interest in the study of finding closed-form solutions of difference equations and systems of difference equations. Some of the forms of solutions of these equations are representable via wellknown integer sequences such as Fibonacci numbers (see, for example [26,32]), Horadam numbers (see, for example, [30,31]), Lucas numbers (see, for example [25,27,33]), Pell numbers and Padovan numbers (see, for example [34][35][36]), But in this paper, we present the solution in the form of Lucas sequences.…”

Section: Introductionmentioning

confidence: 99%

Global Behavior of Solutions to a Higher-Dimensional System of Difference Equations with Lucas Numbers Coefficients

Berkal,

Navarro,

Abo-Zeid

2024

MCA

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Section: Introductionmentioning

confidence: 99%

Global Behavior of Solutions to a Higher-Dimensional System of Difference Equations with Lucas Numbers Coefficients

Berkal,

Navarro,

Abo-Zeid

2024

MCA

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“…Because, some of the solution forms of these equations are even expressible in terms of well-known integer sequences. As it can be seen from the references, there are many papers on such these studies from several authors, see [6,7,8,9,10,11,12,13,21].…”

Section: Introductionmentioning

confidence: 99%

Bazi Fark Denklemleri̇ni̇n Ayarlanmiş Jacobsthal-Padovan Sayilari İle İli̇şki̇li̇ Tam Çözümleri̇

Göcen

2022

Kırklareli Üniversitesi Mühendislik Ve Fen Bilimleri Dergisi

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Bu makalede, bazı rasyonel fark denklemlerinin ayarlanmış Jacobsthal-Padovan sayıları ile çözümlerinin formunu elde ediyoruz. Kesin çözümler ile ayarlanmış Jacobsthal-Padovan sayıları arasında bir ilişki buluyoruz. Literatürün dışında, çözümlerin bu iyi bilinen diziler ile ilişkili kapalı formunu üstel fonksiyonlar kullanarak veriyoruz. Ayrıca, bu fark denklemlerinin denge noktasının asimptotik davranışını inceliyoruz.

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Solvability and solution character of a hyperbolic cotangent-type difference equation of second-order

Tollu,

Yazlık

2024

J. Appl. Math. Comput.

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In the present study, we show that the second-order nonlinear difference equation $$\begin{aligned} x_{n}=\frac{x_{n-1}x_{n-2}-a}{x_{n-1}-x_{n-2}},\ n\in \mathbb {N}_{0}, \end{aligned}$$ x n = x n - 1 x n - 2 - a x n - 1 - x n - 2 , n ∈ N 0 , where $$a\in \left[ 0,\infty \right) $$ a ∈ 0 , ∞ and the initial values $$x_{-2}$$ x - 2 , $$x_{-1}$$ x - 1 are real numbers, is solvable in closed form and that solutions can be analyzed in detail by the Fibonacci numbers.

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General solutions to systems of difference equations and some of their representations

Cited by 8 publications

References 24 publications

Global Behavior of Solutions to a Higher-Dimensional System of Difference Equations with Lucas Numbers Coefficients

Global Behavior of Solutions to a Higher-Dimensional System of Difference Equations with Lucas Numbers Coefficients

Bazi Fark Denklemleri̇ni̇n Ayarlanmiş Jacobsthal-Padovan Sayilari İle İli̇şki̇li̇ Tam Çözümleri̇

Solvability and solution character of a hyperbolic cotangent-type difference equation of second-order

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