THE EXACT SOLUTIONS OF SOME DIFFERENCE EQUATIONS ASSOCIATED WITH ADJUSTED JACOBSTHAL-PADOVAN NUMBERS

Year 2022, , 1 - 14, 30.06.2022

Melih Göcen

https://doi.org/10.34186/klujes.1078836

Abstract

In this paper, we obtain the form of the solutions of some rational difference equations via adjusted Jacobsthal-Padovan numbers. We find a relation between the exact solutions and the adjusted Jacobsthal-Padovan numbers. Apart from the literature, we give the closed form of the solutions associated with these well-known integer sequence using exponential functions. Furthermore, we investigate the asymptotic behavior of the equilibrium point of the solutions of these difference equations.

Keywords

Difference equation, Form of the solutions, Stability, Jacobsthal-Padovan numbers

BAZI FARK DENKLEMLERİNİN AYARLANMIŞ JACOBSTHAL-PADOVAN SAYILARI İLE İLİŞKİLİ TAM ÇÖZÜMLERİ

Abstract

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.

Keywords

Fark denklemi, Çözümlerin formu, Karalılık, Jacobsthal-Padovan sayıları.

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