Solving Zhou chaotic system using fourth-order Runge-Kutta method

Most of scientific problems and natural phenomena can be modeled by chaotic systems of ordinary differential equations. These problems can be solved by using various methods. In this paper, we are interested to test the Runge-Kutta method of order four on the Zhou chaotic system. This system is a...

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Main Authors: Mohd Roslan, Umuu ’Atiqah, Salleh, Zabidin, Kilicman, Adem
Format: Article
Language:English
English
Published: IDOSI Publications 2013
Online Access:http://psasir.upm.edu.my/id/eprint/30147/
http://psasir.upm.edu.my/id/eprint/30147/1/Solving%20Zhou%20chaotic%20system%20using%20fourth.pdf
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author Mohd Roslan, Umuu ’Atiqah
Salleh, Zabidin
Kilicman, Adem
author_facet Mohd Roslan, Umuu ’Atiqah
Salleh, Zabidin
Kilicman, Adem
author_sort Mohd Roslan, Umuu ’Atiqah
building UPM Institutional Repository
collection Online Access
description Most of scientific problems and natural phenomena can be modeled by chaotic systems of ordinary differential equations. These problems can be solved by using various methods. In this paper, we are interested to test the Runge-Kutta method of order four on the Zhou chaotic system. This system is a new three-dimensional autonomous chaotic system. Numerical comparisons are made between the Runge-Kutta of order four and the Euler’s method. Comparisons were also done between the RK4 methods but with different time steps. It has been observed that the accuracy of RK4 solutions can be increased by decreasing the time step. Our work shows that RK4 method successfully can solve the Zhou system and figures are given for different number of iterations with corresponding range of time, t.
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language English
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publishDate 2013
publisher IDOSI Publications
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spelling upm-301472015-10-08T07:51:07Z http://psasir.upm.edu.my/id/eprint/30147/ Solving Zhou chaotic system using fourth-order Runge-Kutta method Mohd Roslan, Umuu ’Atiqah Salleh, Zabidin Kilicman, Adem Most of scientific problems and natural phenomena can be modeled by chaotic systems of ordinary differential equations. These problems can be solved by using various methods. In this paper, we are interested to test the Runge-Kutta method of order four on the Zhou chaotic system. This system is a new three-dimensional autonomous chaotic system. Numerical comparisons are made between the Runge-Kutta of order four and the Euler’s method. Comparisons were also done between the RK4 methods but with different time steps. It has been observed that the accuracy of RK4 solutions can be increased by decreasing the time step. Our work shows that RK4 method successfully can solve the Zhou system and figures are given for different number of iterations with corresponding range of time, t. IDOSI Publications 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30147/1/Solving%20Zhou%20chaotic%20system%20using%20fourth.pdf Mohd Roslan, Umuu ’Atiqah and Salleh, Zabidin and Kilicman, Adem (2013) Solving Zhou chaotic system using fourth-order Runge-Kutta method. World Applied Sciences Journal, 21 (6). pp. 939-944. ISSN 1818-4952; ESSN: 1991-6426 http://www.idosi.org/wasj/wasj21(6)2013.htm 10.5829/idosi.wasj.2013.21.6.2915 English
spellingShingle Mohd Roslan, Umuu ’Atiqah
Salleh, Zabidin
Kilicman, Adem
Solving Zhou chaotic system using fourth-order Runge-Kutta method
title Solving Zhou chaotic system using fourth-order Runge-Kutta method
title_full Solving Zhou chaotic system using fourth-order Runge-Kutta method
title_fullStr Solving Zhou chaotic system using fourth-order Runge-Kutta method
title_full_unstemmed Solving Zhou chaotic system using fourth-order Runge-Kutta method
title_short Solving Zhou chaotic system using fourth-order Runge-Kutta method
title_sort solving zhou chaotic system using fourth-order runge-kutta method
url http://psasir.upm.edu.my/id/eprint/30147/
http://psasir.upm.edu.my/id/eprint/30147/
http://psasir.upm.edu.my/id/eprint/30147/
http://psasir.upm.edu.my/id/eprint/30147/1/Solving%20Zhou%20chaotic%20system%20using%20fourth.pdf