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...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/939367 |
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| author | K. W. Moo N. Senu F. Ismail M. Suleiman |
| author_facet | K. W. Moo N. Senu F. Ismail M. Suleiman |
| author_sort | K. W. Moo |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-33411238c921480ba24a14b12f84c399 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-33411238c921480ba24a14b12f84c3992025-02-03T06:05:10ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/939367939367New Phase-Fitted and Amplification-Fitted Fourth-Order and Fifth-Order Runge-Kutta-Nyström Methods for Oscillatory ProblemsK. W. Moo0N. Senu1F. Ismail2M. Suleiman3Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaTwo 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.http://dx.doi.org/10.1155/2013/939367 |
| spellingShingle | K. W. Moo N. Senu F. Ismail M. Suleiman New Phase-Fitted and Amplification-Fitted Fourth-Order and Fifth-Order Runge-Kutta-Nyström Methods for Oscillatory Problems Abstract and Applied Analysis |
| 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 nystrom methods for oscillatory problems |
| url | http://dx.doi.org/10.1155/2013/939367 |
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