SOLVABILITY OF A FOUR DIMENSIONAL SYSTEM OF DIFFERENCE EQUATIONS

Abstract

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.