Embedded explicit two-step runge-kutta-nystr¨om for solving special second-order IVPs
A third-order three-stage explicit Two-step Runge-Kutta-Nystr¨om (TSRKN) method embedded into fourth-order three-stage TSRKN method is developed to solve special second-order initial value problems (IVPs) directly. The stability of the method is investigated. Numerical results are obtained by solvin...
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| Format: | Article |
| Language: | English |
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Hikari Ltd
2018
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| Online Access: | http://eprints.uthm.edu.my/5538/ http://eprints.uthm.edu.my/5538/1/AJ%202018%20%28567%29.pdf |
| _version_ | 1848888577612578816 |
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| author | Md Ariffin, Latifah Senu, Norazak Suleiman, Mohamed Abdul Majid, Zanariah |
| author_facet | Md Ariffin, Latifah Senu, Norazak Suleiman, Mohamed Abdul Majid, Zanariah |
| author_sort | Md Ariffin, Latifah |
| building | UTHM Institutional Repository |
| collection | Online Access |
| description | A third-order three-stage explicit Two-step Runge-Kutta-Nystr¨om (TSRKN) method embedded into fourth-order three-stage TSRKN method is developed to solve special second-order initial value problems (IVPs) directly. The stability of the method is investigated. Numerical results are obtained by solving a standard set of test problems, which then reduced to first-order system when solved using Runge-Kutta (RK) method and comparison are made with existing RK method with same order using variable step-size. The results clearly showed the advantage and the efficiency of the new method. |
| first_indexed | 2025-11-15T20:12:30Z |
| format | Article |
| id | uthm-5538 |
| institution | Universiti Tun Hussein Onn Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T20:12:30Z |
| publishDate | 2018 |
| publisher | Hikari Ltd |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | uthm-55382022-01-13T07:25:57Z http://eprints.uthm.edu.my/5538/ Embedded explicit two-step runge-kutta-nystr¨om for solving special second-order IVPs Md Ariffin, Latifah Senu, Norazak Suleiman, Mohamed Abdul Majid, Zanariah T Technology (General) QA299.6-433 Analysis A third-order three-stage explicit Two-step Runge-Kutta-Nystr¨om (TSRKN) method embedded into fourth-order three-stage TSRKN method is developed to solve special second-order initial value problems (IVPs) directly. The stability of the method is investigated. Numerical results are obtained by solving a standard set of test problems, which then reduced to first-order system when solved using Runge-Kutta (RK) method and comparison are made with existing RK method with same order using variable step-size. The results clearly showed the advantage and the efficiency of the new method. Hikari Ltd 2018 Article PeerReviewed text en http://eprints.uthm.edu.my/5538/1/AJ%202018%20%28567%29.pdf Md Ariffin, Latifah and Senu, Norazak and Suleiman, Mohamed and Abdul Majid, Zanariah (2018) Embedded explicit two-step runge-kutta-nystr¨om for solving special second-order IVPs. Applied Mathematical Sciences, 8 (94). pp. 4655-4673. ISSN 1312-885X http://dx.doi.org/10.12988/ams.2014.46403 |
| spellingShingle | T Technology (General) QA299.6-433 Analysis Md Ariffin, Latifah Senu, Norazak Suleiman, Mohamed Abdul Majid, Zanariah Embedded explicit two-step runge-kutta-nystr¨om for solving special second-order IVPs |
| title | Embedded explicit two-step runge-kutta-nystr¨om for solving special second-order IVPs |
| title_full | Embedded explicit two-step runge-kutta-nystr¨om for solving special second-order IVPs |
| title_fullStr | Embedded explicit two-step runge-kutta-nystr¨om for solving special second-order IVPs |
| title_full_unstemmed | Embedded explicit two-step runge-kutta-nystr¨om for solving special second-order IVPs |
| title_short | Embedded explicit two-step runge-kutta-nystr¨om for solving special second-order IVPs |
| title_sort | embedded explicit two-step runge-kutta-nystr¨om for solving special second-order ivps |
| topic | T Technology (General) QA299.6-433 Analysis |
| url | http://eprints.uthm.edu.my/5538/ http://eprints.uthm.edu.my/5538/ http://eprints.uthm.edu.my/5538/1/AJ%202018%20%28567%29.pdf |