# Analysis of Exact Solutions to Some Systems of Difference Equations

### Abstract

Some nonlinear difference equations can be sometimes solved analytically using manual iteration which begins with some given initial conditions. Obtaining next iterations always depends on the previous ones. Through this paper, we utilize the manual iteration in investigating the exact solutions of the following recursive sequences $x_{n+1}=\frac{y_{n-5}x_{n-8}}{y_{n-2}(-1-y_{n-5}x_{n-8})},\ \ \ \ \ y_{n+1}% =\frac{x_{n-5}y_{n-8}}{x_{n-2}\left( \pm1\pm x_{n-5}y_{n-8}\right) },$ where the initial conditions $x_{\delta},\ y_{\delta},\ \delta\in \{0,1,...,8\}$ are non-zero real numbers. Some numerical solutions are also presented in some figures to show the behaviour of the solutions.### Downloads

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Copyright (c) 2019 Mohammed Almatrafi, Marwa M. Alzubaidi

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