Optimized hybrid methods for solving oscillatory second order initial value problems
Two-step optimized hybrid methods of order five and order six are developed for the integration of second order oscillatory initial value problems. The optimized hybrid method (OHMs) are based on the existing nonzero dissipative hybrid methods. Phase-lag, dissipation or amplification error, and the...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/45709/1/HYBRID.pdf |
| _version_ | 1796974570557669376 |
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| author | Senu, Norazak Suleiman, Mohamed Ismail, Fudziah Ahmad, S. Z. |
| author_facet | Senu, Norazak Suleiman, Mohamed Ismail, Fudziah Ahmad, S. Z. |
| author_sort | Senu, Norazak |
| collection | UPM |
| description | Two-step optimized hybrid methods of order five and order six are developed for the integration of second order oscillatory initial value problems. The optimized hybrid method (OHMs) are based on the existing nonzero dissipative hybrid methods. Phase-lag, dissipation or amplification error, and the differentiation of the phase-lag relations are required to obtain the methods. Phase-fitted methods based on the same nonzero dissipative hybrid methods are also constructed. Numerical results show that OHMs are more accurate compared to the phase-fitted methods and some well-known methods appeared in the scientific literature in solving oscillating second order initial value problems. It is also found that the nonzero dissipative hybrid methods are more suitable to be optimized than phase-fitted methods. |
| first_indexed | 2024-03-06T08:58:58Z |
| format | Article |
| id | upm.eprints-45709 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:58:58Z |
| publishDate | 2015 |
| publisher | Hindawi Publishing |
| record_format | dspace |
| spelling | upm.eprints-457092021-01-20T17:47:34Z http://psasir.upm.edu.my/id/eprint/45709/ Optimized hybrid methods for solving oscillatory second order initial value problems Senu, Norazak Suleiman, Mohamed Ismail, Fudziah Ahmad, S. Z. Two-step optimized hybrid methods of order five and order six are developed for the integration of second order oscillatory initial value problems. The optimized hybrid method (OHMs) are based on the existing nonzero dissipative hybrid methods. Phase-lag, dissipation or amplification error, and the differentiation of the phase-lag relations are required to obtain the methods. Phase-fitted methods based on the same nonzero dissipative hybrid methods are also constructed. Numerical results show that OHMs are more accurate compared to the phase-fitted methods and some well-known methods appeared in the scientific literature in solving oscillating second order initial value problems. It is also found that the nonzero dissipative hybrid methods are more suitable to be optimized than phase-fitted methods. Hindawi Publishing 2015 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/45709/1/HYBRID.pdf Senu, Norazak and Suleiman, Mohamed and Ismail, Fudziah and Ahmad, S. Z. (2015) Optimized hybrid methods for solving oscillatory second order initial value problems. Discrete Dynamics in Nature and Society. pp. 1-11. ISSN 1026-0226; ESSN: 1607-887X https://www.hindawi.com/journals/ddns/2015/217578/ 10.1155/2015/217578 |
| spellingShingle | Senu, Norazak Suleiman, Mohamed Ismail, Fudziah Ahmad, S. Z. Optimized hybrid methods for solving oscillatory second order initial value problems |
| title | Optimized hybrid methods for solving oscillatory second order initial value problems |
| title_full | Optimized hybrid methods for solving oscillatory second order initial value problems |
| title_fullStr | Optimized hybrid methods for solving oscillatory second order initial value problems |
| title_full_unstemmed | Optimized hybrid methods for solving oscillatory second order initial value problems |
| title_short | Optimized hybrid methods for solving oscillatory second order initial value problems |
| title_sort | optimized hybrid methods for solving oscillatory second order initial value problems |
| url | http://psasir.upm.edu.my/id/eprint/45709/1/HYBRID.pdf |
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