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

Fractal and Fractional

article

Mohamed Adel¹  Mohamed M. Khader³  Salman Algelany¹ 

[1] Department of Mathematics, Faculty of Science, Islamic University of Madinah;Department of Mathematics, Faculty of Science, Cairo University;Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University;Department of Mathematics, Faculty of Science, Benha University

关键词: chaotic Lorenz model;    Caputo fractional derivative;    Appell-Changhee polynomials;    spectral collocation method;    RK434A12;    41A30;    47H10;    65N20;   

DOI  :  10.3390/fractalfract7050398

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY