Block hybrid method with trigonometric-fitting for solving oscillatory problems
In this paper, we develop algebraic order conditions for two-point block hybrid method up to order five using the approach of B-series. Based on the order conditions, we derive fifth order two-point block explicit hybrid method for solving special second order ordinary differential equations (ODEs),...
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/15279/ http://psasir.upm.edu.my/id/eprint/15279/1/Block%20hybrid%20method%20with%20trigonometric-fitting%20for%20solving%20oscillatory%20problems.pdf |
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| author | Ismail, Fudziah Ahmad, Sufia Zulfa Jikantoro, Yusuf Dauda Senu, Norazak |
| author_facet | Ismail, Fudziah Ahmad, Sufia Zulfa Jikantoro, Yusuf Dauda Senu, Norazak |
| author_sort | Ismail, Fudziah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, we develop algebraic order conditions for two-point block hybrid method up to order five using the approach of B-series. Based on the order conditions, we derive fifth order two-point block explicit hybrid method for solving special second order ordinary differential equations (ODEs), where the existing explicit hybrid method of order five is used to be the method at the first point. The method is then trigonometrically fitted so that it can be suitable for solving highly oscillatory problems arising from special second order ODEs. The new trigonometrically-fitted block method is tested using a set of oscillatory problems over a very large interval. Numerical results clearly showed the superiority of the method in terms of accuracy and execution time compared to other existing methods in the scientific literature. |
| first_indexed | 2025-11-15T08:02:13Z |
| format | Article |
| id | upm-15279 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:02:13Z |
| publishDate | 2018 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-152792019-05-09T01:41:26Z http://psasir.upm.edu.my/id/eprint/15279/ Block hybrid method with trigonometric-fitting for solving oscillatory problems Ismail, Fudziah Ahmad, Sufia Zulfa Jikantoro, Yusuf Dauda Senu, Norazak In this paper, we develop algebraic order conditions for two-point block hybrid method up to order five using the approach of B-series. Based on the order conditions, we derive fifth order two-point block explicit hybrid method for solving special second order ordinary differential equations (ODEs), where the existing explicit hybrid method of order five is used to be the method at the first point. The method is then trigonometrically fitted so that it can be suitable for solving highly oscillatory problems arising from special second order ODEs. The new trigonometrically-fitted block method is tested using a set of oscillatory problems over a very large interval. Numerical results clearly showed the superiority of the method in terms of accuracy and execution time compared to other existing methods in the scientific literature. Penerbit Universiti Kebangsaan Malaysia 2018 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/15279/1/Block%20hybrid%20method%20with%20trigonometric-fitting%20for%20solving%20oscillatory%20problems.pdf Ismail, Fudziah and Ahmad, Sufia Zulfa and Jikantoro, Yusuf Dauda and Senu, Norazak (2018) Block hybrid method with trigonometric-fitting for solving oscillatory problems. Sains Malaysiana, 47 (9). pp. 2223-2230. ISSN 0026-6039 http://www.ukm.my/jsm/english_journals/vol47num9_2018/contentsVol47num9_2018.html 10.17576/jsm-2018-4709-33 |
| spellingShingle | Ismail, Fudziah Ahmad, Sufia Zulfa Jikantoro, Yusuf Dauda Senu, Norazak Block hybrid method with trigonometric-fitting for solving oscillatory problems |
| title | Block hybrid method with trigonometric-fitting for solving oscillatory problems |
| title_full | Block hybrid method with trigonometric-fitting for solving oscillatory problems |
| title_fullStr | Block hybrid method with trigonometric-fitting for solving oscillatory problems |
| title_full_unstemmed | Block hybrid method with trigonometric-fitting for solving oscillatory problems |
| title_short | Block hybrid method with trigonometric-fitting for solving oscillatory problems |
| title_sort | block hybrid method with trigonometric-fitting for solving oscillatory problems |
| url | http://psasir.upm.edu.my/id/eprint/15279/ http://psasir.upm.edu.my/id/eprint/15279/ http://psasir.upm.edu.my/id/eprint/15279/ http://psasir.upm.edu.my/id/eprint/15279/1/Block%20hybrid%20method%20with%20trigonometric-fitting%20for%20solving%20oscillatory%20problems.pdf |