Qualitative Behavior of Solutions of Tenth-Order Recursive Sequence Equation

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 Un+1=Un−9Un−5Un−1/Un−7Un−3±1±Un−9Un−5Un−1, n≥0, where the initial values are positive real numbers. Stability and periodicity are also investigated.