A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different Methods
This study aims to find a solution to the symmetry chaotic jerk system by using a new ABC-FD scheme and the NILM method. The findings of the supplied methods have been compared to Runge–Kutta’s fourth order (RK4). It was discovered that the suggested techniques gave results comparable to the RK4 met...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/11/1991 |
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| author | Abdulrahman B. M. Alzahrani Mohamed A. Abdoon Mohamed Elbadri Mohammed Berir Diaa Eldin Elgezouli |
| author_facet | Abdulrahman B. M. Alzahrani Mohamed A. Abdoon Mohamed Elbadri Mohammed Berir Diaa Eldin Elgezouli |
| author_sort | Abdulrahman B. M. Alzahrani |
| collection | DOAJ |
| description | This study aims to find a solution to the symmetry chaotic jerk system by using a new ABC-FD scheme and the NILM method. The findings of the supplied methods have been compared to Runge–Kutta’s fourth order (RK4). It was discovered that the suggested techniques gave results comparable to the RK4 method. Our primary goal is to develop effective methods for addressing symmetrical, chaotic systems. Using ABC-FD and NILM presents innovative approaches for comprehending and effectively handling intricate dynamics. The findings of this study have significant significance for addressing the occurrence of chaotic behavior in diverse scientific and engineering contexts. This research significantly contributes to fractional calculus and its various applications. The application of ABC-FD, which can identify chaotic behavior, makes our work stand out. This novel approach contributes to advancing research in nonlinear dynamics and fractional calculus. The present study not only offers a resolution to the problem of symmetric chaotic jerk systems but also presents a framework that may be applied to tackle analogous challenges in several domains. The techniques outlined in this paper facilitate the development and computational analysis of prospective fractional models, thereby contributing to the progress of scientific and engineering disciplines. |
| first_indexed | 2024-03-09T16:26:06Z |
| format | Article |
| id | doaj.art-f8ef50a6718a4193be12d1bf7825b4fb |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T16:26:06Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-f8ef50a6718a4193be12d1bf7825b4fb2023-11-24T15:08:40ZengMDPI AGSymmetry2073-89942023-10-011511199110.3390/sym15111991A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different MethodsAbdulrahman B. M. Alzahrani0Mohamed A. Abdoon1Mohamed Elbadri2Mohammed Berir3Diaa Eldin Elgezouli4Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaDepartment of Basic Sciences, Common First Year Deanship, King Saud University, Riyadh 12373, Saudi ArabiaDepartment of Mathematics, Faculty of Sciences and Arts, Jouf University, Tubarjal 74713, Saudi ArabiaDepartment of Mathematics, Faculty of Science and Arts, Al-Baha University, Baljurashi 65622, Saudi ArabiaDepartment of Basic Sciences, Common First Year Deanship, King Saud University, Riyadh 12373, Saudi ArabiaThis study aims to find a solution to the symmetry chaotic jerk system by using a new ABC-FD scheme and the NILM method. The findings of the supplied methods have been compared to Runge–Kutta’s fourth order (RK4). It was discovered that the suggested techniques gave results comparable to the RK4 method. Our primary goal is to develop effective methods for addressing symmetrical, chaotic systems. Using ABC-FD and NILM presents innovative approaches for comprehending and effectively handling intricate dynamics. The findings of this study have significant significance for addressing the occurrence of chaotic behavior in diverse scientific and engineering contexts. This research significantly contributes to fractional calculus and its various applications. The application of ABC-FD, which can identify chaotic behavior, makes our work stand out. This novel approach contributes to advancing research in nonlinear dynamics and fractional calculus. The present study not only offers a resolution to the problem of symmetric chaotic jerk systems but also presents a framework that may be applied to tackle analogous challenges in several domains. The techniques outlined in this paper facilitate the development and computational analysis of prospective fractional models, thereby contributing to the progress of scientific and engineering disciplines.https://www.mdpi.com/2073-8994/15/11/1991numerical solutionsthe Atangana–Baleanu fractional derivativenew iterative Laplace methodchaos |
| spellingShingle | Abdulrahman B. M. Alzahrani Mohamed A. Abdoon Mohamed Elbadri Mohammed Berir Diaa Eldin Elgezouli A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different Methods Symmetry numerical solutions the Atangana–Baleanu fractional derivative new iterative Laplace method chaos |
| title | A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different Methods |
| title_full | A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different Methods |
| title_fullStr | A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different Methods |
| title_full_unstemmed | A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different Methods |
| title_short | A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different Methods |
| title_sort | comparative numerical study of the symmetry chaotic jerk system with a hyperbolic sine function via two different methods |
| topic | numerical solutions the Atangana–Baleanu fractional derivative new iterative Laplace method chaos |
| url | https://www.mdpi.com/2073-8994/15/11/1991 |
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