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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Main Authors:	Fudziah Ismail, Sufia Zulfa Ahmad, Jikantoro, Yusuf Dauda, Norazak Senu
Format:	Article
Language:	English
Published:	Penerbit Universiti Kebangsaan Malaysia 2018
Online Access:	http://journalarticle.ukm.my/12417/ http://journalarticle.ukm.my/12417/ http://journalarticle.ukm.my/12417/1/33%20Fudziah%20Ismail.pdf

id	ukm-12417
recordtype	eprints
spelling	ukm-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
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
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.
format	Article
author	Fudziah Ismail, Sufia Zulfa Ahmad, Jikantoro, Yusuf Dauda Norazak Senu,
spellingShingle	Fudziah Ismail, Sufia Zulfa Ahmad, Jikantoro, Yusuf Dauda Norazak Senu, Block hybrid method with trigonometric-fitting for solving oscillatory problems
author_facet	Fudziah Ismail, Sufia Zulfa Ahmad, Jikantoro, Yusuf Dauda Norazak Senu,
author_sort	Fudziah Ismail,
title	Block hybrid method with trigonometric-fitting for solving oscillatory problems
title_short	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_sort	block hybrid method with trigonometric-fitting for solving oscillatory problems
publisher	Penerbit Universiti Kebangsaan Malaysia
publishDate	2018
url	http://journalarticle.ukm.my/12417/ http://journalarticle.ukm.my/12417/ http://journalarticle.ukm.my/12417/1/33%20Fudziah%20Ismail.pdf
first_indexed	2023-09-18T20:02:33Z
last_indexed	2023-09-18T20:02:33Z
_version_	1777406945670463488

Block hybrid method with trigonometric-fitting for solving oscillatory problems

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