Numerical Simulation for a High-Dimensional Chaotic Lorenz System Based on Gegenbauer Wavelet Polynomials

被引：27

作者：

Alqhtani, Manal ^{[1
]}

Khader, Mohamed M. ^{[2
,3
]}

Saad, Khaled Mohammed ^{[1
]}

机构：

[1] Najran Univ, Coll Arts & Sci, Dept Math, Najran 55461, Saudi Arabia

[2] Imam Mohammad Ibn Saud Islamic Univ IMSIU, Coll Sci, Dept Math & Stat, Riyadh 11566, Saudi Arabia

[3] Benha Univ, Fac Sci, Dept Math, Banha 13511, Egypt

来源：

MATHEMATICS | 2023年 / 11卷 / 02期

关键词：

chaotic Lorenz model; Caputo differential operator; Gegenbauer wavelet polynomials; SCM; fourth-order Runge-Kutta method; MODEL;

D O I：

10.3390/math11020472

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide an effective simulation to investigate the solution behavior of nine-dimensional chaos for the fractional (Caputo-sense) Lorenz system using a new approximate technique of the spectral collocation method (SCM) depending on the properties of Gegenbauer wavelet polynomials (GWPs). This technique reduces the given problem to a non-linear system of algebraic equations. We satisfy the accuracy and efficiency of the proposed method by computing the residual error function. The numerical solutions obtained are compared with the results obtained by implementing the Runge-Kutta method of order four. The results show that the given procedure is an easily applied and efficient tool to simulate this model.

引用

页数：12

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