Analysis of Exact Solutions to Some Systems of Difference Equations

  • Mohammed Almatrafi M. B. Almatrafi
  • Marwa M. Alzubaidi
Keywords: Difference Equations, Systems of Difference Equations, Exact Solution, Stability, Periodicity

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.  

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Published
2019-08-30
How to Cite
Almatrafi, M., & Alzubaidi, M. M. (2019). Analysis of Exact Solutions to Some Systems of Difference Equations. MathLAB Journal, 3, 96-117. Retrieved from http://purkh.com/index.php/mathlab/article/view/478
Section
Research Articles