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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/943293 |
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| _version_ | 1832564098679701504 |
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| author | Hassan Saberi Nik Paulo Rebelo |
| author_facet | Hassan Saberi Nik Paulo Rebelo |
| author_sort | Hassan Saberi Nik |
| collection | DOAJ |
| 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 | Article |
| id | doaj-art-015746bf71784e9bac59dde6d02b4219 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-015746bf71784e9bac59dde6d02b42192025-02-03T01:11:48ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/943293943293Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex SystemsHassan Saberi Nik0Paulo Rebelo1Department of Mathematics, Islamic Azad University, Mashhad Branch, Mashhad, IranDepartamento de Matemática, Universidade da Beira Interior, 6201-001 Covilhã, PortugalWe 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.http://dx.doi.org/10.1155/2014/943293 |
| spellingShingle | Hassan Saberi Nik Paulo Rebelo Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems The Scientific World Journal |
| 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 |
| url | http://dx.doi.org/10.1155/2014/943293 |
| work_keys_str_mv | AT hassansaberinik multistagespectralrelaxationmethodforsolvingthehyperchaoticcomplexsystems AT paulorebelo multistagespectralrelaxationmethodforsolvingthehyperchaoticcomplexsystems |