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Multistage spectral relaxation method for solving the hyperchaotic complex systems.

Saberi Nik H, Rebelo P - ScientificWorldJournal (2014)

Bottom Line: 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.We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Islamic Azad University, Mashhad Branch, Mashhad, Iran.

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.

Show MeSH
Comparison between the MSRM and ode45 results for the hyperchaotic complex Lorenz system.
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Related In: Results  -  Collection


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fig1: Comparison between the MSRM and ode45 results for the hyperchaotic complex Lorenz system.

Mentions: Through numerical experimentation, it was determined that N = 6 collocation points and 5 iterations of the MSRM scheme at each interval were sufficient to give accurate results in each [ti−1, ti] interval. Tables 1 and 2 show a comparison of the solutions of the hyperchaotic complex Lorenz system computed by the MSRM and ode45. In Figures 1, 2, and 3, the MSRM graphical results are also compared with ode45 and good agreement is observed. The MRSM phase portraits in Figures 4 and 5 were also found to be exactly the same as those computed using ode45. This shows that the proposed MSRM is a valid tool for solving the hyperchaotic complex Lorenz system.


Multistage spectral relaxation method for solving the hyperchaotic complex systems.

Saberi Nik H, Rebelo P - ScientificWorldJournal (2014)

Comparison between the MSRM and ode45 results for the hyperchaotic complex Lorenz system.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4216706&req=5

fig1: Comparison between the MSRM and ode45 results for the hyperchaotic complex Lorenz system.
Mentions: Through numerical experimentation, it was determined that N = 6 collocation points and 5 iterations of the MSRM scheme at each interval were sufficient to give accurate results in each [ti−1, ti] interval. Tables 1 and 2 show a comparison of the solutions of the hyperchaotic complex Lorenz system computed by the MSRM and ode45. In Figures 1, 2, and 3, the MSRM graphical results are also compared with ode45 and good agreement is observed. The MRSM phase portraits in Figures 4 and 5 were also found to be exactly the same as those computed using ode45. This shows that the proposed MSRM is a valid tool for solving the hyperchaotic complex Lorenz system.

Bottom Line: 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.We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Islamic Azad University, Mashhad Branch, Mashhad, Iran.

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.

Show MeSH