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The Scientific World Journal
Volume 2014 (2014), Article ID 943293, 10 pages
http://dx.doi.org/10.1155/2014/943293
Research Article

Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems

1Department of Mathematics, Islamic Azad University, Mashhad Branch, Mashhad, Iran
2Departamento de Matemática, Universidade da Beira Interior, 6201-001 Covilhã, Portugal

Received 4 August 2014; Accepted 12 September 2014; Published 16 October 2014

Academic Editor: Fazlollah Soleymani

Copyright © 2014 Hassan Saberi Nik and Paulo Rebelo. 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.

Abstract

We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results.