High-Dimensional Chaotic Lorenz System: Numerical Treatment Using Changhee Polynomials of the Appell Type

Abstract

Presenting and simulating the numerical treatment of the nine-dimensional fractional chaotic Lorenz system is the goal of this work. The spectral collocation method (SCM), which makes use of Changhee polynomials of the Appell type, is the suggested approximation technique to achieve this goal. A rough formula for the Caputo fractional derivative is first derived, and it is used to build the numerical strategy for the suggested model’s solution. This procedure creates a system of algebraic equations from the model that was provided. We validate the effectiveness and precision of the provided approach by evaluating the residual error function (REF). We compare the results obtained with the fourth-order Runge–Kutta technique and other existing published work. The outcomes demonstrate that the technique used is a simple and effective tool for simulating such models.

Keywords

• chaotic Lorenz model
• Caputo fractional derivative
• Appell-Changhee polynomials
• spectral collocation method
• RK4