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

Author

Listed:
  • 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
    Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt)

  • Khaled Mohammed Saad

    (Department of Mathematics, College of Arts and Sciences, Najran University, Najran 55461, Saudi Arabia)

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.

Suggested Citation

  • Manal Alqhtani & Mohamed M. Khader & Khaled Mohammed Saad, 2023. "Numerical Simulation for a High-Dimensional Chaotic Lorenz System Based on Gegenbauer Wavelet Polynomials," Mathematics, MDPI, vol. 11(2), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:472-:d:1037170
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    References listed on IDEAS

    as
    1. Neslihan Ozdemir & Aydin Secer & Mustafa Bayram, 2019. "The Gegenbauer Wavelets-Based Computational Methods for the Coupled System of Burgers’ Equations with Time-Fractional Derivative," Mathematics, MDPI, vol. 7(6), pages 1-15, May.
    2. Xiaofei Zhou & Junmei Li & Yulan Wang & Wei Zhang, 2019. "Numerical Simulation of a Class of Hyperchaotic System Using Barycentric Lagrange Interpolation Collocation Method," Complexity, Hindawi, vol. 2019, pages 1-13, February.
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