New explicit trigonometrically-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for periodic initial value problems
In this work, we derive two new Runge-Kutta-Nyström (RKN) methods for solving periodic second order ordinary differential equations. We constructed these methods based on the RKN method of three-stage fourth-order derived by Garcia and RKN method of four-stage fifth-order derived by Hairer. The nume...
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| Format: | Article |
| Language: | English |
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Academic Publications
2016
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| Online Access: | http://psasir.upm.edu.my/id/eprint/51865/ http://psasir.upm.edu.my/id/eprint/51865/1/New%20explicit%20trigonometrically-fitted%20fourth-order%20and%20fifth-order%20Runge-Kutta-Nystr%C3%B6m%20methods%20for%20periodic%20initial%20value%20problems.pdf |
| _version_ | 1848851949261160448 |
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| author | Demba, Musa Ahmed Senu, Norazak Ismail, Fudziah |
| author_facet | Demba, Musa Ahmed Senu, Norazak Ismail, Fudziah |
| author_sort | Demba, Musa Ahmed |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this work, we derive two new Runge-Kutta-Nyström (RKN) methods for solving periodic second order ordinary differential equations. We constructed these methods based on the RKN method of three-stage fourth-order derived by Garcia and RKN method of four-stage fifth-order derived by Hairer. The numerical results show that the efficiency of the new methods is more than the other existing methods. |
| first_indexed | 2025-11-15T10:30:18Z |
| format | Article |
| id | upm-51865 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:30:18Z |
| publishDate | 2016 |
| publisher | Academic Publications |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-518652017-05-02T08:06:05Z http://psasir.upm.edu.my/id/eprint/51865/ New explicit trigonometrically-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for periodic initial value problems Demba, Musa Ahmed Senu, Norazak Ismail, Fudziah In this work, we derive two new Runge-Kutta-Nyström (RKN) methods for solving periodic second order ordinary differential equations. We constructed these methods based on the RKN method of three-stage fourth-order derived by Garcia and RKN method of four-stage fifth-order derived by Hairer. The numerical results show that the efficiency of the new methods is more than the other existing methods. Academic Publications 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/51865/1/New%20explicit%20trigonometrically-fitted%20fourth-order%20and%20fifth-order%20Runge-Kutta-Nystr%C3%B6m%20methods%20for%20periodic%20initial%20value%20problems.pdf Demba, Musa Ahmed and Senu, Norazak and Ismail, Fudziah (2016) New explicit trigonometrically-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for periodic initial value problems. International Journal of Pure and Applied Mathematics, 109 (3). pp. 557-571. ISSN 1311-8080; ESSN: 1314-3395 http://www.ijpam.eu/contents/2016-109-3/6/index.html |
| spellingShingle | Demba, Musa Ahmed Senu, Norazak Ismail, Fudziah New explicit trigonometrically-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for periodic initial value problems |
| title | New explicit trigonometrically-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for periodic initial value problems |
| title_full | New explicit trigonometrically-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for periodic initial value problems |
| title_fullStr | New explicit trigonometrically-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for periodic initial value problems |
| title_full_unstemmed | New explicit trigonometrically-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for periodic initial value problems |
| title_short | New explicit trigonometrically-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for periodic initial value problems |
| title_sort | new explicit trigonometrically-fitted fourth-order and fifth-order runge-kutta-nyström methods for periodic initial value problems |
| url | http://psasir.upm.edu.my/id/eprint/51865/ http://psasir.upm.edu.my/id/eprint/51865/ http://psasir.upm.edu.my/id/eprint/51865/1/New%20explicit%20trigonometrically-fitted%20fourth-order%20and%20fifth-order%20Runge-Kutta-Nystr%C3%B6m%20methods%20for%20periodic%20initial%20value%20problems.pdf |