Solutions formulas for some general systems of difference equations

In this work, we show that the system of difference equationsxn+1=(ayn-2xn-1yn+bxn-1yn-2+cyn-2+d)/(yn-2xn-1yn),yn+1=(axn-2yn-1xn+byn-1xn-2+cxn-2+d)/(xn-2yn-1xn),where n belongs to the set of positive integer numbers, x-2, x-1, x0, y-2, y-1 and y0 are arbitrary nonzero real numbers, and the parameters a, b, c and d are arbitrary real numbers with d nonzero can be solved in a closed form.We will see that when a = b = c = d = 1, the solutions are expressed using the famous Tetranacci numbers. In particular, the results obtained here extend those in our recent work.

show abstract

“….17) and -Some parts of the results of this paper were used in the reference [2] in which the authors have generalized the system (1.2).…”

Section: Proof Of the Main Theoremmentioning

confidence: 99%

On a system of difference equations of third order solved in closed form

Akrour

Touafek²,

Halim³

2021

J. Innov. Appl. Math. Comput. Sci

Self Cite

View full text Add to dashboard Cite

show abstract

“…The theory of system of difference equations improved until today. Recently, there has been great interest in studying difference equation or difference equations systems [1][2][3][5][6][7]9,[12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Solvability of a Four Dimensional System of Difference Equations

DEVECİOĞLU,

KARA

2024

Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler

Self Cite

View full text Add to dashboard Cite

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.

show abstract