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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...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Hindawi Publishing Corporation
2014
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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. |
format | Online Article Text |
id | pubmed-4216706 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2014 |
publisher | Hindawi Publishing Corporation |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT saberinikhassan multistagespectralrelaxationmethodforsolvingthehyperchaoticcomplexsystems AT rebelopaulo multistagespectralrelaxationmethodforsolvingthehyperchaoticcomplexsystems |