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Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems

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 t...

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Detalles Bibliográficos
Autores principales: Saberi Nik, Hassan, Rebelo, Paulo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4216706/
https://www.ncbi.nlm.nih.gov/pubmed/25386624
http://dx.doi.org/10.1155/2014/943293
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author Saberi Nik, Hassan
Rebelo, Paulo
author_facet Saberi Nik, Hassan
Rebelo, Paulo
author_sort Saberi Nik, Hassan
collection PubMed
description 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.
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spelling pubmed-42167062014-11-10 Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems Saberi Nik, Hassan Rebelo, Paulo ScientificWorldJournal Research Article 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. Hindawi Publishing Corporation 2014 2014-10-16 /pmc/articles/PMC4216706/ /pubmed/25386624 http://dx.doi.org/10.1155/2014/943293 Text en Copyright © 2014 H. Saberi Nik and P. Rebelo. https://creativecommons.org/licenses/by/3.0/ 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.
spellingShingle Research Article
Saberi Nik, Hassan
Rebelo, Paulo
Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems
title Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems
title_full Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems
title_fullStr Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems
title_full_unstemmed Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems
title_short Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems
title_sort multistage spectral relaxation method for solving the hyperchaotic complex systems
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4216706/
https://www.ncbi.nlm.nih.gov/pubmed/25386624
http://dx.doi.org/10.1155/2014/943293
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