New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for oscillatory problems
Two new Runge-Kutta-Nyström (RKN) methods are constructed for solving second-order differential equations with oscillatory solutions. These two new methods are constructed based on two existing RKN methods. Firstly, a three-stage fourth-order Garcia’s RKN method. Another method is Hairer’s RKN metho...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30120/ http://psasir.upm.edu.my/id/eprint/30120/1/30120.pdf |
| _version_ | 1848846588225519616 |
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| author | Moo, Kwong Wing Senu, Norazak Ismail, Fudziah Suleiman, Mohamed |
| author_facet | Moo, Kwong Wing Senu, Norazak Ismail, Fudziah Suleiman, Mohamed |
| author_sort | Moo, Kwong Wing |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Two new Runge-Kutta-Nyström (RKN) methods are constructed for solving second-order differential equations with oscillatory solutions. These two new methods are constructed based on two existing RKN methods. Firstly, a three-stage fourth-order Garcia’s RKN method. Another method is Hairer’s RKN method of four-stage fifth-order. Both new derived methods have two variable coefficients with phase-lag of order infinity and zero amplification error (zero dissipative). Numerical tests are performed and the results show that the new methods are more accurate than the other methods in the literature. |
| first_indexed | 2025-11-15T09:05:06Z |
| format | Article |
| id | upm-30120 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:05:06Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-301202017-10-20T04:14:15Z http://psasir.upm.edu.my/id/eprint/30120/ New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for oscillatory problems Moo, Kwong Wing Senu, Norazak Ismail, Fudziah Suleiman, Mohamed Two new Runge-Kutta-Nyström (RKN) methods are constructed for solving second-order differential equations with oscillatory solutions. These two new methods are constructed based on two existing RKN methods. Firstly, a three-stage fourth-order Garcia’s RKN method. Another method is Hairer’s RKN method of four-stage fifth-order. Both new derived methods have two variable coefficients with phase-lag of order infinity and zero amplification error (zero dissipative). Numerical tests are performed and the results show that the new methods are more accurate than the other methods in the literature. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30120/1/30120.pdf Moo, Kwong Wing and Senu, Norazak and Ismail, Fudziah and Suleiman, Mohamed (2013) New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for oscillatory problems. Abstract and Applied Analysis, 2013. art. no. 939367. pp. 1-9. ISSN 1085-3375; ESSN: 1687-0409 http://www.hindawi.com/journals/aaa/2013/939367/ 10.1155/2013/939367 |
| spellingShingle | Moo, Kwong Wing Senu, Norazak Ismail, Fudziah Suleiman, Mohamed New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for oscillatory problems |
| title | New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for oscillatory problems |
| title_full | New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for oscillatory problems |
| title_fullStr | New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for oscillatory problems |
| title_full_unstemmed | New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for oscillatory problems |
| title_short | New phase-fitted and amplification-fitted fourth-order and fifth-order Runge-Kutta-Nyström methods for oscillatory problems |
| title_sort | new phase-fitted and amplification-fitted fourth-order and fifth-order runge-kutta-nyström methods for oscillatory problems |
| url | http://psasir.upm.edu.my/id/eprint/30120/ http://psasir.upm.edu.my/id/eprint/30120/ http://psasir.upm.edu.my/id/eprint/30120/ http://psasir.upm.edu.my/id/eprint/30120/1/30120.pdf |