Directly solving special second order delay differential equations using Runge-Kutta-Nystrom method
Runge-Kutta-Nyström (RKN) method is adapted for solving the special second order delay differential equations (DDEs). The stability polynomial is obtained when this method is used for solving linear second order delay differential equation. A standard set of test problems is solved using the method...
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| Format: | Article |
| Language: | English English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30053/ http://psasir.upm.edu.my/id/eprint/30053/1/Directly%20solving%20special%20second%20order%20delay%20differential%20equations%20using%20Runge.pdf |
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| author | Mechee, Mohammed Ismail, Fudziah Senu, Norazak Siri, Zailan |
| author_facet | Mechee, Mohammed Ismail, Fudziah Senu, Norazak Siri, Zailan |
| author_sort | Mechee, Mohammed |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Runge-Kutta-Nyström (RKN) method is adapted for solving the special second order delay differential equations (DDEs). The stability polynomial is obtained when this method is used for solving linear second order delay differential equation. A standard set of test problems is solved using the method together with a cubic interpolation for evaluating the delay terms. The same set of problems is reduced to a system of first order delay differential equations and then solved using the existing Runge-Kutta (RK) method. Numerical results show that the RKN method is more efficient in terms of accuracy and computational time when compared to RK method. The methods are applied to a well-known problem involving delay differential equations, that is, the Mathieu problem. The numerical comparison shows that both methods are in a good agreement. |
| first_indexed | 2025-11-15T09:04:48Z |
| format | Article |
| id | upm-30053 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T09:04:48Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
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| spelling | upm-300532015-10-08T00:53:50Z http://psasir.upm.edu.my/id/eprint/30053/ Directly solving special second order delay differential equations using Runge-Kutta-Nystrom method Mechee, Mohammed Ismail, Fudziah Senu, Norazak Siri, Zailan Runge-Kutta-Nyström (RKN) method is adapted for solving the special second order delay differential equations (DDEs). The stability polynomial is obtained when this method is used for solving linear second order delay differential equation. A standard set of test problems is solved using the method together with a cubic interpolation for evaluating the delay terms. The same set of problems is reduced to a system of first order delay differential equations and then solved using the existing Runge-Kutta (RK) method. Numerical results show that the RKN method is more efficient in terms of accuracy and computational time when compared to RK method. The methods are applied to a well-known problem involving delay differential equations, that is, the Mathieu problem. The numerical comparison shows that both methods are in a good agreement. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30053/1/Directly%20solving%20special%20second%20order%20delay%20differential%20equations%20using%20Runge.pdf Mechee, Mohammed and Ismail, Fudziah and Senu, Norazak and Siri, Zailan (2013) Directly solving special second order delay differential equations using Runge-Kutta-Nystrom method. Mathematical Problems in Engineering, 2013 (830317). pp. 1-7. ISSN 1024-123X http://www.hindawi.com/journals/mpe/2013/830317/ 10.1155/2013/830317 English |
| spellingShingle | Mechee, Mohammed Ismail, Fudziah Senu, Norazak Siri, Zailan Directly solving special second order delay differential equations using Runge-Kutta-Nystrom method |
| title | Directly solving special second order delay differential equations using Runge-Kutta-Nystrom method |
| title_full | Directly solving special second order delay differential equations using Runge-Kutta-Nystrom method |
| title_fullStr | Directly solving special second order delay differential equations using Runge-Kutta-Nystrom method |
| title_full_unstemmed | Directly solving special second order delay differential equations using Runge-Kutta-Nystrom method |
| title_short | Directly solving special second order delay differential equations using Runge-Kutta-Nystrom method |
| title_sort | directly solving special second order delay differential equations using runge-kutta-nystrom method |
| url | http://psasir.upm.edu.my/id/eprint/30053/ http://psasir.upm.edu.my/id/eprint/30053/ http://psasir.upm.edu.my/id/eprint/30053/ http://psasir.upm.edu.my/id/eprint/30053/1/Directly%20solving%20special%20second%20order%20delay%20differential%20equations%20using%20Runge.pdf |