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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| Format: | Article |
| Language: | English English |
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IDOSI Publications
2013
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| 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 |
| _version_ | 1848846595603300352 |
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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. |
| first_indexed | 2025-11-15T09:05:13Z |
| format | Article |
| id | upm-30147 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T09:05:13Z |
| publishDate | 2013 |
| publisher | IDOSI Publications |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |