Solving directly two point boundary value problems using direct multistep method

In this paper we consider solving directly two point boundary value problems (BVPs) for second-order ordinary differential equations (ODEs). We are concerned with solving this problem using multistep method in term of backward difference formula and approximating the solutions with the shooting meth...

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Main Authors:	Mahanum Diana Jafri, Mohamed Suleiman, Zanariah Abdul Majid, Zarina Bibi Ibrahim
Format:	Article
Language:	English
Published:	Universiti Kebangsaan Malaysia 2009
Online Access:	http://journalarticle.ukm.my/13/ http://journalarticle.ukm.my/13/ http://journalarticle.ukm.my/13/1/

id	ukm-13
recordtype	eprints
spelling	ukm-132016-12-14T06:26:11Z http://journalarticle.ukm.my/13/ Solving directly two point boundary value problems using direct multistep method Mahanum Diana Jafri, Mohamed Suleiman, Zanariah Abdul Majid, Zarina Bibi Ibrahim, In this paper we consider solving directly two point boundary value problems (BVPs) for second-order ordinary differential equations (ODEs). We are concerned with solving this problem using multistep method in term of backward difference formula and approximating the solutions with the shooting method. Most of the existence researches involved BVPs will reduce the problem to a system of first order ODEs. This approach is very well established but it obviously will enlarge the system of first order equations. However, the direct multistep method in this paper will be utilised to obtain a series solution of the initial value problems directly without reducing to first order equations. The numerical results show that the proposed method with shooting method can produce good results. Universiti Kebangsaan Malaysia 2009-10 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/13/1/ Mahanum Diana Jafri, and Mohamed Suleiman, and Zanariah Abdul Majid, and Zarina Bibi Ibrahim, (2009) Solving directly two point boundary value problems using direct multistep method. Sains Malaysiana, 38 (5). pp. 723-728. ISSN 0126-6039 http://www.ukm.my/~jsm/kandungan.html
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 consider solving directly two point boundary value problems (BVPs) for second-order ordinary differential equations (ODEs). We are concerned with solving this problem using multistep method in term of backward difference formula and approximating the solutions with the shooting method. Most of the existence researches involved BVPs will reduce the problem to a system of first order ODEs. This approach is very well established but it obviously will enlarge the system of first order equations. However, the direct multistep method in this paper will be utilised to obtain a series solution of the initial value problems directly without reducing to first order equations. The numerical results show that the proposed method with shooting method can produce good results.
format	Article
author	Mahanum Diana Jafri, Mohamed Suleiman, Zanariah Abdul Majid, Zarina Bibi Ibrahim,
spellingShingle	Mahanum Diana Jafri, Mohamed Suleiman, Zanariah Abdul Majid, Zarina Bibi Ibrahim, Solving directly two point boundary value problems using direct multistep method
author_facet	Mahanum Diana Jafri, Mohamed Suleiman, Zanariah Abdul Majid, Zarina Bibi Ibrahim,
author_sort	Mahanum Diana Jafri,
title	Solving directly two point boundary value problems using direct multistep method
title_short	Solving directly two point boundary value problems using direct multistep method
title_full	Solving directly two point boundary value problems using direct multistep method
title_fullStr	Solving directly two point boundary value problems using direct multistep method
title_full_unstemmed	Solving directly two point boundary value problems using direct multistep method
title_sort	solving directly two point boundary value problems using direct multistep method
publisher	Universiti Kebangsaan Malaysia
publishDate	2009
url	http://journalarticle.ukm.my/13/ http://journalarticle.ukm.my/13/ http://journalarticle.ukm.my/13/1/
first_indexed	2023-09-18T19:01:03Z
last_indexed	2023-09-18T19:01:03Z
_version_	1777403076111499264

Solving directly two point boundary value problems using direct multistep method

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