GENERALIZED NUMERICAL SOLUTIONS OF NONLINEAR DIFFERENCE EQUATIONS AND THEIR CHARACTERISTICS
Keywords:
nonlinear difference equations, general solutions, numerical examplesDOI:
https://doi.org/10.17654/0972096025004Abstract
The general solutions of nonlinear difference equations are presented in this paper along with an analysis of their boundedness, convergence, and other characteristics. The primary goal of this research is to obtain some general solutions for the nonlinear difference equations listed below:
$$
X_{m+1}=\frac{X_{m-7}}{1-X_{m-7} \Upsilon_{m-3}}, \quad \Upsilon_{m+1}=\frac{\Upsilon_{m-7}}{ \pm 1 \pm \Upsilon_{m-7} X_{m-3}}
$$
where $X_{-7}, X_{-6}, X_{-5}, X_{-4}, X_{-3}, X_{-2}, X_{-1}, X_0, \Upsilon_{-7}, \Upsilon_{-6}$, $\Upsilon_{-5}, \Upsilon_{-4}, \Upsilon_{-3}, \Upsilon_{-2}, \Upsilon_{-1}$ and $\Upsilon_0$ are all real numbers ( $\left.\mathfrak{R}\right)$ that rely on the initial conditions. Four numerical examples are shown to demonstrate the caliber of the outcomes utilizing the MATLAB and Mathematica softwares. Our primary findings are both specific on the approaches of solving the equations and some extremely general ones.
Received: February 4, 2025
Accepted: March 28, 2025
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