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Abstract and Applied Analysis
Volume 2012, Article ID 203461, 18 pages
Research Article

Solving Hyperchaotic Systems Using the Spectral Relaxation Method

1School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg, Scottsville 3209, South Africa
2Department of Mathematics, University of Johannesburg, P.O. Box 17011, Doornfontein 2028, South Africa

Received 10 October 2012; Accepted 28 November 2012

Academic Editor: Narcisa C. Apreutesei

Copyright © 2012 S. S. Motsa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new multistage numerical method based on blending a Gauss-Siedel relaxation method and Chebyshev pseudospectral method, for solving complex dynamical systems exhibiting hyperchaotic behavior, is presented. The proposed method, called the multistage spectral relaxation method (MSRM), is applied for the numerical solution of three hyperchaotic systems, namely, the Chua, Chen, and Rabinovich-Fabrikant systems. To demonstrate the performance of the method, results are presented in tables and diagrams and compared to results obtained using a Runge-Kutta-(4,5)-based MATLAB solver, ode45, and other previously published results.