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),...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2018
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| Online Access: | http://journalarticle.ukm.my/12417/1/33%20Fudziah%20Ismail.pdf |
| _version_ | 1796931674847576064 |
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| author | Fudziah Ismail, Sufia Zulfa Ahmad, Jikantoro, Yusuf Dauda Norazak Senu, |
| author_facet | Fudziah Ismail, Sufia Zulfa Ahmad, Jikantoro, Yusuf Dauda Norazak Senu, |
| author_sort | Fudziah Ismail, |
| collection | UKM |
| 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 | 2024-03-06T04:21:29Z |
| format | Article |
| id | ukm.eprints-12417 |
| institution | Universiti Kebangsaan Malaysia |
| language | English |
| last_indexed | 2024-03-06T04:21:29Z |
| publishDate | 2018 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| record_format | dspace |
| spelling | ukm.eprints-124172018-12-07T23:47:56Z http://journalarticle.ukm.my/12417/ Block hybrid method with trigonometric-fitting for solving oscillatory problems Fudziah Ismail, Sufia Zulfa Ahmad, Jikantoro, Yusuf Dauda Norazak Senu, 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 2018-09 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/12417/1/33%20Fudziah%20Ismail.pdf Fudziah Ismail, and Sufia Zulfa Ahmad, and Jikantoro, Yusuf Dauda and Norazak Senu, (2018) Block hybrid method with trigonometric-fitting for solving oscillatory problems. Sains Malaysiana, 47 (9). pp. 2223-2230. ISSN 0126-6039 http://www.ukm.my/jsm/malay_journals/jilid47bil9_2018/KandunganJilid47Bil9_2018.htm |
| spellingShingle | Fudziah Ismail, Sufia Zulfa Ahmad, Jikantoro, Yusuf Dauda Norazak Senu, 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://journalarticle.ukm.my/12417/1/33%20Fudziah%20Ismail.pdf |
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