SOLVABILITY OF A FOUR DIMENSIONAL SYSTEM OF DIFFERENCE EQUATIONS

Yıl 2024, Cilt: 12 Sayı: 1, 62 - 74, 27.02.2024

Şule Devecioğlu Merve Kara

https://doi.org/10.20290/estubtdb.1403701

Öz

In this study, we investigate the following four-dimensional difference equations system
{█(u_n=(αu_(n-3) t_(n-2)+β)/(γv_(n-1) t_(n-2) u_(n-3) ), @v_n=(αv_(n-3) u_(n-2)+β)/(γw_(n-1) u_(n-2) v_(n-3) ),n∈N_0,@w_n=(αw_(n-3) v_(n-2)+β)/(γt_(n-1) v_(n-2) w_(n-3) ), @t_n=(αt_(n-3) w_(n-2)+β)/(γu_(n-1) w_(n-2) t_(n-3) ), )┤
where the initial values u_(-d),v_(-d),w_(-d),t_(-d), d∈{1,2,3} and the parameters α,β,γ are real numbers. Then, we obtain the solutions of system of third-order difference equations in explicit form. In addition, the solutions according to some special cases of the parameters are examined. Finally, numerical examples are given to demonstrate the theoretical results.

Anahtar Kelimeler

Periodicity, System of difference equation, Solution

Kaynakça

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