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

Manal Alqhtani, Mohamed M. Khader and Khaled Mohammed Saad ()
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Manal Alqhtani: Department of Mathematics, College of Arts and Sciences, Najran University, Najran 55461, Saudi Arabia
Mohamed M. Khader: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia
Khaled Mohammed Saad: Department of Mathematics, College of Arts and Sciences, Najran University, Najran 55461, Saudi Arabia

Mathematics, 2023, vol. 11, issue 2, 1-12

Abstract: 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.

Keywords: chaotic Lorenz model; Caputo differential operator; Gegenbauer wavelet polynomials; SCM; fourth-order Runge–Kutta method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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