Numerical algorithm of block method for general second order ODEs using variable step size

This paper outlines an alternative algorithm for solving general second order ordinary differential equations (ODEs). Normally, the numerical method was designed for solving higher order ODEs by converting it into an n-dimensional first order equations with implementation of constant step length. Ne...

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Main Authors:	Nazreen Waeleh, Zanariah Abdul Majid
Format:	Article
Language:	English
Published:	Penerbit Universiti Kebangsaan Malaysia 2017
Online Access:	http://journalarticle.ukm.my/11070/ http://journalarticle.ukm.my/11070/ http://journalarticle.ukm.my/11070/1/16%20Nazreen%20Waeleh.pdf

id	ukm-11070
recordtype	eprints
spelling	ukm-110702017-12-12T04:49:04Z http://journalarticle.ukm.my/11070/ Numerical algorithm of block method for general second order ODEs using variable step size Nazreen Waeleh, Zanariah Abdul Majid, This paper outlines an alternative algorithm for solving general second order ordinary differential equations (ODEs). Normally, the numerical method was designed for solving higher order ODEs by converting it into an n-dimensional first order equations with implementation of constant step length. Nevertheless, this involved a lot of computational complexity which led to consumption a lot of time. Consequently, a direct block multistep method with utilization of variable step size strategy is proposed. This method was developed for computing the solution at four points simultaneously and the derivation based on numerical integration as well as using interpolation approach. The convergence of the proposed method is justified under suitable conditions of stability and consistency. Five numerical examples are considered and some comparisons are made with the existing methods for demonstrating the validity and reliability of the proposed algorithm. Penerbit Universiti Kebangsaan Malaysia 2017-05 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/11070/1/16%20Nazreen%20Waeleh.pdf Nazreen Waeleh, and Zanariah Abdul Majid, (2017) Numerical algorithm of block method for general second order ODEs using variable step size. Sains Malaysiana, 46 (5). pp. 817-824. ISSN 0126-6039 http://www.ukm.my/jsm/english_journals/vol46num5_2017/contentsVol46num5_2017.html
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
description	This paper outlines an alternative algorithm for solving general second order ordinary differential equations (ODEs). Normally, the numerical method was designed for solving higher order ODEs by converting it into an n-dimensional first order equations with implementation of constant step length. Nevertheless, this involved a lot of computational complexity which led to consumption a lot of time. Consequently, a direct block multistep method with utilization of variable step size strategy is proposed. This method was developed for computing the solution at four points simultaneously and the derivation based on numerical integration as well as using interpolation approach. The convergence of the proposed method is justified under suitable conditions of stability and consistency. Five numerical examples are considered and some comparisons are made with the existing methods for demonstrating the validity and reliability of the proposed algorithm.
format	Article
author	Nazreen Waeleh, Zanariah Abdul Majid,
spellingShingle	Nazreen Waeleh, Zanariah Abdul Majid, Numerical algorithm of block method for general second order ODEs using variable step size
author_facet	Nazreen Waeleh, Zanariah Abdul Majid,
author_sort	Nazreen Waeleh,
title	Numerical algorithm of block method for general second order ODEs using variable step size
title_short	Numerical algorithm of block method for general second order ODEs using variable step size
title_full	Numerical algorithm of block method for general second order ODEs using variable step size
title_fullStr	Numerical algorithm of block method for general second order ODEs using variable step size
title_full_unstemmed	Numerical algorithm of block method for general second order ODEs using variable step size
title_sort	numerical algorithm of block method for general second order odes using variable step size
publisher	Penerbit Universiti Kebangsaan Malaysia
publishDate	2017
url	http://journalarticle.ukm.my/11070/ http://journalarticle.ukm.my/11070/ http://journalarticle.ukm.my/11070/1/16%20Nazreen%20Waeleh.pdf
first_indexed	2023-09-18T19:59:16Z
last_indexed	2023-09-18T19:59:16Z
_version_	1777406739045416960

Numerical algorithm of block method for general second order ODEs using variable step size

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