Development of high-order adaptive multi-step Runge–Kutta–Nyström method for solving special second-order ODEs
Runge–Kutta–Nyström (RKN) methods are extensively used to obtain approximate solutions of ordinary differential equations (ODEs). Specifically, they are widely used to directly solve second-order ODEs of the special form. Although the derivation of new higher-order methods with fewer numbers of func...
| Main Authors: | , , , |
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| Format: | Article |
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Elsevier
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/105714/ |
| _version_ | 1848864587861983232 |
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| author | Abdulsalam, Athraa Senu, Norazak Majid, Zanariah Abdul Long, Nik Mohd Asri Nik |
| author_facet | Abdulsalam, Athraa Senu, Norazak Majid, Zanariah Abdul Long, Nik Mohd Asri Nik |
| author_sort | Abdulsalam, Athraa |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Runge–Kutta–Nyström (RKN) methods are extensively used to obtain approximate solutions of ordinary differential equations (ODEs). Specifically, they are widely used to directly solve second-order ODEs of the special form. Although the derivation of new higher-order methods with fewer numbers of function evaluations is of great importance in increasing the precision and effectiveness of the methods, however, this is rarely done due to the difficulty or complexity of some derivations. This study focuses on constructing a 7(5) pair of embedded multi-step Runge–Kutta–Nyström (EMSN) method with lower stages for the numerical solutions of special second-order ODEs. An adaptive step size formulation using an embedded procedure is considered, and the numerical findings reveal that the new embedded pair outperforms existing Runge–Kutta (RK) pairs in terms of the minimum number of functions evaluations. © 2023 International Association for Mathematics and Computers in Simulation (IMACS) |
| first_indexed | 2025-11-15T13:51:11Z |
| format | Article |
| id | upm-105714 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:51:11Z |
| publishDate | 2024 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1057142024-03-25T07:42:02Z http://psasir.upm.edu.my/id/eprint/105714/ Development of high-order adaptive multi-step Runge–Kutta–Nyström method for solving special second-order ODEs Abdulsalam, Athraa Senu, Norazak Majid, Zanariah Abdul Long, Nik Mohd Asri Nik Runge–Kutta–Nyström (RKN) methods are extensively used to obtain approximate solutions of ordinary differential equations (ODEs). Specifically, they are widely used to directly solve second-order ODEs of the special form. Although the derivation of new higher-order methods with fewer numbers of function evaluations is of great importance in increasing the precision and effectiveness of the methods, however, this is rarely done due to the difficulty or complexity of some derivations. This study focuses on constructing a 7(5) pair of embedded multi-step Runge–Kutta–Nyström (EMSN) method with lower stages for the numerical solutions of special second-order ODEs. An adaptive step size formulation using an embedded procedure is considered, and the numerical findings reveal that the new embedded pair outperforms existing Runge–Kutta (RK) pairs in terms of the minimum number of functions evaluations. © 2023 International Association for Mathematics and Computers in Simulation (IMACS) Elsevier 2024-01 Article PeerReviewed Abdulsalam, Athraa and Senu, Norazak and Majid, Zanariah Abdul and Long, Nik Mohd Asri Nik (2024) Development of high-order adaptive multi-step Runge–Kutta–Nyström method for solving special second-order ODEs. Mathematics and Computers in Simulation, 216. pp. 104-125. ISSN 0378-4754 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85171628857&doi=10.1016%2fj.matcom.2023.09.006&partnerID=40&md5=7cae4e9ec29d1f9dee853d2864f71bed 10.1016/j.matcom.2023.09.006 |
| spellingShingle | Abdulsalam, Athraa Senu, Norazak Majid, Zanariah Abdul Long, Nik Mohd Asri Nik Development of high-order adaptive multi-step Runge–Kutta–Nyström method for solving special second-order ODEs |
| title | Development of high-order adaptive multi-step Runge–Kutta–Nyström method for solving special second-order ODEs |
| title_full | Development of high-order adaptive multi-step Runge–Kutta–Nyström method for solving special second-order ODEs |
| title_fullStr | Development of high-order adaptive multi-step Runge–Kutta–Nyström method for solving special second-order ODEs |
| title_full_unstemmed | Development of high-order adaptive multi-step Runge–Kutta–Nyström method for solving special second-order ODEs |
| title_short | Development of high-order adaptive multi-step Runge–Kutta–Nyström method for solving special second-order ODEs |
| title_sort | development of high-order adaptive multi-step runge–kutta–nyström method for solving special second-order odes |
| url | http://psasir.upm.edu.my/id/eprint/105714/ http://psasir.upm.edu.my/id/eprint/105714/ http://psasir.upm.edu.my/id/eprint/105714/ |