Qualitative Behavior of Solutions of Tenth-Order Recursive Sequence Equation. (14th February 2022) - Elsayed, E. M.; Alofi, B. S.; Khan, Abdul Qadeer
Abstract : Most nonlinear difference equations have exact solutions that are not always possible to obtain theoretically. As a result, a large number of researchers investigate several qualitative aspects of difference equations in order to predict their lengthy behavior. The goal of our research is to obtain the solutions of a tenth-order difference equation U n + 1 = U n − 9 U n − 5 U n − 1 / U n − 7 U n − 3 ± 1 ± U n − 9 U n − 5 U n − 1,   n ≥ 0, where the initial values are positive real numbers. Stability and periodicity are also investigated.