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Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly

In this paper, a direct integration implicit variable step size method in the form of Adams Moulton Method is developed for solving directly the second order system of ordinary differential equations (ODEs) using variable step size. The existing multistep method involves the computations of the divi...

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Main Authors: Zanariah Abdul Majid ,, Mohamed Suleiman,
Format: Article
Published: Universiti Kebangsaan Malaysia 2006
Online Access:http://journalarticle.ukm.my/3991/
http://www.ukm.my/jsm/english_journals/vol35num2_2006/vol35num2_06page63-68.html
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spelling my-ukm.journal.39912012-03-28T03:47:50Z http://journalarticle.ukm.my/3991/ Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly Zanariah Abdul Majid , Mohamed Suleiman, In this paper, a direct integration implicit variable step size method in the form of Adams Moulton Method is developed for solving directly the second order system of ordinary differential equations (ODEs) using variable step size. The existing multistep method involves the computations of the divided differences and integration coefficients in the code when using the variable step size or variable step size and order. The idea of developing this method is to store all the coefficients involved in the code. Thus, this strategy can avoid the lengthy computation of the coefficients during the implementation of the code as well as to improve the execution time. Numerical results are given to compare the efficiency of the developed method with the 1-point method of variable step size and order code (1PDVSO) in Omar (1999). Universiti Kebangsaan Malaysia 2006-12 Article PeerReviewed Zanariah Abdul Majid , and Mohamed Suleiman, (2006) Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly. Sains Malaysiana, 35 (2). pp. 63-68. ISSN 0126-6039 http://www.ukm.my/jsm/english_journals/vol35num2_2006/vol35num2_06page63-68.html
institution Universiti Kebangsaan Malaysia
building Perpustakaan Tun Sri Lanang Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Kebangsaan Malaysia
content_source UKM Journal Article Repository
url_provider http://journalarticle.ukm.my/
description In this paper, a direct integration implicit variable step size method in the form of Adams Moulton Method is developed for solving directly the second order system of ordinary differential equations (ODEs) using variable step size. The existing multistep method involves the computations of the divided differences and integration coefficients in the code when using the variable step size or variable step size and order. The idea of developing this method is to store all the coefficients involved in the code. Thus, this strategy can avoid the lengthy computation of the coefficients during the implementation of the code as well as to improve the execution time. Numerical results are given to compare the efficiency of the developed method with the 1-point method of variable step size and order code (1PDVSO) in Omar (1999).
format Article
author Zanariah Abdul Majid ,
Mohamed Suleiman,
spellingShingle Zanariah Abdul Majid ,
Mohamed Suleiman,
Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly
author_facet Zanariah Abdul Majid ,
Mohamed Suleiman,
author_sort Zanariah Abdul Majid ,
title Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly
title_short Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly
title_full Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly
title_fullStr Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly
title_full_unstemmed Direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly
title_sort direct integration implicit variable steps method for solving higher order systems of ordinary differential equations directly
publisher Universiti Kebangsaan Malaysia
publishDate 2006
url http://journalarticle.ukm.my/3991/
http://www.ukm.my/jsm/english_journals/vol35num2_2006/vol35num2_06page63-68.html
_version_ 1643735921909039104
score 13.211869

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