Solution of higher order ODEs using backward difference method.

The current numerical technique for solving a system of higher-order ordinary differential equations (ODEs) is to reduce it to a system of first-order equations then solving it using first-order ODE methods. Here, we propose a method to solve higher-order ODEs directly. The formulae will be derived...

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Main Authors:	Suleiman, Mohamed, Ibrahim, Zarina Bibi, Rasedee, Ahmad Fadly Nurullah
Format:	Article
Language:	English
Published:	Hindawi Publishing Corporation 2011
Online Access:	http://psasir.upm.edu.my/id/eprint/25025/ http://www.hindawi.com/
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Institution:	Universiti Putra Malaysia
Language:	English

id	my.upm.eprints.25025
record_format	eprints
spelling	my.upm.eprints.250252013-08-02T08:03:44Z http://psasir.upm.edu.my/id/eprint/25025/ Solution of higher order ODEs using backward difference method. Suleiman, Mohamed Ibrahim, Zarina Bibi Rasedee, Ahmad Fadly Nurullah The current numerical technique for solving a system of higher-order ordinary differential equations (ODEs) is to reduce it to a system of first-order equations then solving it using first-order ODE methods. Here, we propose a method to solve higher-order ODEs directly. The formulae will be derived in terms of backward difference in a constant stepsize formulation. The method developed will be validated by solving some higher-order ODEs directly with constant stepsize. To simplify the evaluations of the integration coefficients, we find the relationship between various orders. The result presented confirmed our hypothesis. Hindawi Publishing Corporation 2011 Article PeerReviewed Suleiman, Mohamed and Ibrahim, Zarina Bibi and Rasedee, Ahmad Fadly Nurullah (2011) Solution of higher order ODEs using backward difference method. Mathematical Problems in Engineering, 2011 (810324). pp. 1-18. ISSN 1024-123X http://www.hindawi.com/ 10.1155/2011/810324 English
institution	Universiti Putra Malaysia
building	UPM Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	Universiti Putra Malaysia
content_source	UPM Institutional Repository
url_provider	http://psasir.upm.edu.my/
language	English
description	The current numerical technique for solving a system of higher-order ordinary differential equations (ODEs) is to reduce it to a system of first-order equations then solving it using first-order ODE methods. Here, we propose a method to solve higher-order ODEs directly. The formulae will be derived in terms of backward difference in a constant stepsize formulation. The method developed will be validated by solving some higher-order ODEs directly with constant stepsize. To simplify the evaluations of the integration coefficients, we find the relationship between various orders. The result presented confirmed our hypothesis.
format	Article
author	Suleiman, Mohamed Ibrahim, Zarina Bibi Rasedee, Ahmad Fadly Nurullah
spellingShingle	Suleiman, Mohamed Ibrahim, Zarina Bibi Rasedee, Ahmad Fadly Nurullah Solution of higher order ODEs using backward difference method.
author_facet	Suleiman, Mohamed Ibrahim, Zarina Bibi Rasedee, Ahmad Fadly Nurullah
author_sort	Suleiman, Mohamed
title	Solution of higher order ODEs using backward difference method.
title_short	Solution of higher order ODEs using backward difference method.
title_full	Solution of higher order ODEs using backward difference method.
title_fullStr	Solution of higher order ODEs using backward difference method.
title_full_unstemmed	Solution of higher order ODEs using backward difference method.
title_sort	solution of higher order odes using backward difference method.
publisher	Hindawi Publishing Corporation
publishDate	2011
url	http://psasir.upm.edu.my/id/eprint/25025/ http://www.hindawi.com/
_version_	1643828536042061824

Solution of higher order ODEs using backward difference method.

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