Embedded explicit two-step Runge-Kutta-Nystrom 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 re-sults are obtained by solv...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Hikari
2014
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| Online Access: | http://eprints.uthm.edu.my/5761/ http://eprints.uthm.edu.my/5761/1/AJ%202017%20%28911%29.pdf |
| _version_ | 1848888630200762368 |
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| author | Ariffin, L. M. Senu, N. Suleiman, M. Majid, Z.A. |
| author_facet | Ariffin, L. M. Senu, N. Suleiman, M. Majid, Z.A. |
| author_sort | Ariffin, L. M. |
| 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 re-sults 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 | 2025-11-15T20:13:20Z |
| format | Article |
| id | uthm-5761 |
| institution | Universiti Tun Hussein Onn Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T20:13:20Z |
| publishDate | 2014 |
| publisher | Hikari |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | uthm-57612022-01-23T04:26:49Z http://eprints.uthm.edu.my/5761/ Embedded explicit two-step Runge-Kutta-Nystrom for solving special second-order IVPs Ariffin, L. M. Senu, N. Suleiman, M. Majid, Z.A. T Technology (General) 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 re-sults 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 2014 Article PeerReviewed text en http://eprints.uthm.edu.my/5761/1/AJ%202017%20%28911%29.pdf Ariffin, L. M. and Senu, N. and Suleiman, M. and Majid, Z.A. (2014) Embedded explicit two-step Runge-Kutta-Nystrom 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) Ariffin, L. M. Senu, N. Suleiman, M. Majid, Z.A. Embedded explicit two-step Runge-Kutta-Nystrom for solving special second-order IVPs |
| title | Embedded explicit two-step Runge-Kutta-Nystrom for solving special second-order IVPs |
| title_full | Embedded explicit two-step Runge-Kutta-Nystrom for solving special second-order IVPs |
| title_fullStr | Embedded explicit two-step Runge-Kutta-Nystrom for solving special second-order IVPs |
| title_full_unstemmed | Embedded explicit two-step Runge-Kutta-Nystrom for solving special second-order IVPs |
| title_short | Embedded explicit two-step Runge-Kutta-Nystrom for solving special second-order IVPs |
| title_sort | embedded explicit two-step runge-kutta-nystrom for solving special second-order ivps |
| topic | T Technology (General) |
| url | http://eprints.uthm.edu.my/5761/ http://eprints.uthm.edu.my/5761/ http://eprints.uthm.edu.my/5761/1/AJ%202017%20%28911%29.pdf |