Approximate solutions of fuzzy hybrid differential system using the RK–Fehlberg scheme of order 5
The article exposes the use of the Runge-Kutta Fehlberg method of order five, a rarely studied methodology, to address the complexity involved in solving fuzzy hybrid differential equations. The study focuses on evaluating the reliability and accuracy of this method in contrast to recognized procedu...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-12-01
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| Series: | Applied Mathematics in Science and Engineering |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/27690911.2024.2376263 |
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| author | Maheswari Rangasamy Prasantha Bharathi Dhandapani Anwar Zeb Ilyas Khan Abdoalrahman S.A. Omer |
| author_facet | Maheswari Rangasamy Prasantha Bharathi Dhandapani Anwar Zeb Ilyas Khan Abdoalrahman S.A. Omer |
| author_sort | Maheswari Rangasamy |
| collection | DOAJ |
| description | The article exposes the use of the Runge-Kutta Fehlberg method of order five, a rarely studied methodology, to address the complexity involved in solving fuzzy hybrid differential equations. The study focuses on evaluating the reliability and accuracy of this method in contrast to recognized procedures, providing a thorough analysis of its performance. The article assesses the effectiveness of the RK-Fehlberg scheme by comparing its results with exact solutions, using thorough analysis and well-supported examples. This comparison analysis highlights the potential of the method to provide more accuracy compared to classic methods like Euler, improved, or modified schemes. The article demonstrates the strength and effectiveness of the method by using numerical examples. This not only helps improve computational techniques for solving fuzzy hybrid systems but also highlights the wide range of applications and reliability of the Runge–Kutta Fehlberg method in mathematical modeling and analysis. |
| format | Article |
| id | doaj-art-5d25653a018a44f09ba19ab2dc1c0f18 |
| institution | Kabale University |
| issn | 2769-0911 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Applied Mathematics in Science and Engineering |
| spelling | doaj-art-5d25653a018a44f09ba19ab2dc1c0f182024-12-06T04:24:24ZengTaylor & Francis GroupApplied Mathematics in Science and Engineering2769-09112024-12-0132110.1080/27690911.2024.2376263Approximate solutions of fuzzy hybrid differential system using the RK–Fehlberg scheme of order 5Maheswari Rangasamy0Prasantha Bharathi Dhandapani1Anwar Zeb2Ilyas Khan3Abdoalrahman S.A. Omer4Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore, IndiaDepartment of Mathematics, Sri Eshwar College of Engineering, Coimbatore, IndiaDepartment of Mathematics, COMSATS University, Islamabad, PakistanDepartment of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, Saudi ArabiaDepartment of Mathematics, College of Education, Elfasher University, Al Fashir, SudanThe article exposes the use of the Runge-Kutta Fehlberg method of order five, a rarely studied methodology, to address the complexity involved in solving fuzzy hybrid differential equations. The study focuses on evaluating the reliability and accuracy of this method in contrast to recognized procedures, providing a thorough analysis of its performance. The article assesses the effectiveness of the RK-Fehlberg scheme by comparing its results with exact solutions, using thorough analysis and well-supported examples. This comparison analysis highlights the potential of the method to provide more accuracy compared to classic methods like Euler, improved, or modified schemes. The article demonstrates the strength and effectiveness of the method by using numerical examples. This not only helps improve computational techniques for solving fuzzy hybrid systems but also highlights the wide range of applications and reliability of the Runge–Kutta Fehlberg method in mathematical modeling and analysis.https://www.tandfonline.com/doi/10.1080/27690911.2024.2376263Hybrid differential equationsfuzzy differential equationsnumerical solutionsrunge-kutta methodrunge-kutta fehlberg method00A05 |
| spellingShingle | Maheswari Rangasamy Prasantha Bharathi Dhandapani Anwar Zeb Ilyas Khan Abdoalrahman S.A. Omer Approximate solutions of fuzzy hybrid differential system using the RK–Fehlberg scheme of order 5 Applied Mathematics in Science and Engineering Hybrid differential equations fuzzy differential equations numerical solutions runge-kutta method runge-kutta fehlberg method 00A05 |
| title | Approximate solutions of fuzzy hybrid differential system using the RK–Fehlberg scheme of order 5 |
| title_full | Approximate solutions of fuzzy hybrid differential system using the RK–Fehlberg scheme of order 5 |
| title_fullStr | Approximate solutions of fuzzy hybrid differential system using the RK–Fehlberg scheme of order 5 |
| title_full_unstemmed | Approximate solutions of fuzzy hybrid differential system using the RK–Fehlberg scheme of order 5 |
| title_short | Approximate solutions of fuzzy hybrid differential system using the RK–Fehlberg scheme of order 5 |
| title_sort | approximate solutions of fuzzy hybrid differential system using the rk fehlberg scheme of order 5 |
| topic | Hybrid differential equations fuzzy differential equations numerical solutions runge-kutta method runge-kutta fehlberg method 00A05 |
| url | https://www.tandfonline.com/doi/10.1080/27690911.2024.2376263 |
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