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

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 tech...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-01, Vol.11 (2), p.472
Main Authors: Alqhtani, Manal, Khader, Mohamed M., Saad, Khaled Mohammed
Format: Article
Language:English
Subjects:
Algebra
Calculus
Caputo differential operator
Chaos theory
chaotic Lorenz model
Chemical reactions
Collocation methods
Error functions
Food science
fourth-order Runge–Kutta method
Gegenbauer wavelet polynomials
Lorenz system
Mathematical models
Nonlinear systems
Numerical analysis
Partial differential equations
Polynomials
Runge-Kutta method
SCM
Simulation
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11020472