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Variable step size block method for solving directly third order ordinary differential equations.

In this study, a two point implicit block direct integration method is derived for solving directly the third order ordinary differential equations (ODEs). This method will estimate the solutions of initial value problems at two points simultaneously on the x-axis using variable step size. The exist...

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Main Authors: Abdul Majid, Zanariah, Suleiman, Mohamed, Azmi, Nurul Asyikin
Format: Article
Language:English
English
Published: Pushpa 2010
Online Access:http://psasir.upm.edu.my/id/eprint/17582/1/Variable%20step%20size%20block%20method%20for%20solving%20directly%20third%20order%20ordinary%20differential%20equations.pdf
http://psasir.upm.edu.my/id/eprint/17582/
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spelling my.upm.eprints.175822015-11-11T07:52:09Z http://psasir.upm.edu.my/id/eprint/17582/ Variable step size block method for solving directly third order ordinary differential equations. Abdul Majid, Zanariah Suleiman, Mohamed Azmi, Nurul Asyikin In this study, a two point implicit block direct integration method is derived for solving directly the third order ordinary differential equations (ODEs). This method will estimate the solutions of initial value problems at two points simultaneously on the x-axis using variable step size. The existence multistep method involves the computations of the divided differences and integration coefficients in the code when using variable step size or variable step size and order. The proposed block method will be presented in a simple form as the Adams Moulton method and the code will store all the constant coefficients of the method. The purpose of the storage is to avoid the computations of the divided differences and the integration coefficients that can be very costly. Although the method is in a simple form but we intend for efficiency and economically. Numerical results were given to compare the efficiency of the developed method in terms of total number of steps, function calls, maximum error and execution times. The results suggested a significant improvement of the proposed method over the existing non-block method. Pushpa 2010 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/17582/1/Variable%20step%20size%20block%20method%20for%20solving%20directly%20third%20order%20ordinary%20differential%20equations.pdf Abdul Majid, Zanariah and Suleiman, Mohamed and Azmi, Nurul Asyikin (2010) Variable step size block method for solving directly third order ordinary differential equations. Far East Journal of Mathematical Sciences, 41 (1). pp. 63-73. ISSN 0972-0871 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
English
description In this study, a two point implicit block direct integration method is derived for solving directly the third order ordinary differential equations (ODEs). This method will estimate the solutions of initial value problems at two points simultaneously on the x-axis using variable step size. The existence multistep method involves the computations of the divided differences and integration coefficients in the code when using variable step size or variable step size and order. The proposed block method will be presented in a simple form as the Adams Moulton method and the code will store all the constant coefficients of the method. The purpose of the storage is to avoid the computations of the divided differences and the integration coefficients that can be very costly. Although the method is in a simple form but we intend for efficiency and economically. Numerical results were given to compare the efficiency of the developed method in terms of total number of steps, function calls, maximum error and execution times. The results suggested a significant improvement of the proposed method over the existing non-block method.
format Article
author Abdul Majid, Zanariah
Suleiman, Mohamed
Azmi, Nurul Asyikin
spellingShingle Abdul Majid, Zanariah
Suleiman, Mohamed
Azmi, Nurul Asyikin
Variable step size block method for solving directly third order ordinary differential equations.
author_facet Abdul Majid, Zanariah
Suleiman, Mohamed
Azmi, Nurul Asyikin
author_sort Abdul Majid, Zanariah
title Variable step size block method for solving directly third order ordinary differential equations.
title_short Variable step size block method for solving directly third order ordinary differential equations.
title_full Variable step size block method for solving directly third order ordinary differential equations.
title_fullStr Variable step size block method for solving directly third order ordinary differential equations.
title_full_unstemmed Variable step size block method for solving directly third order ordinary differential equations.
title_sort variable step size block method for solving directly third order ordinary differential equations.
publisher Pushpa
publishDate 2010
url http://psasir.upm.edu.my/id/eprint/17582/1/Variable%20step%20size%20block%20method%20for%20solving%20directly%20third%20order%20ordinary%20differential%20equations.pdf
http://psasir.upm.edu.my/id/eprint/17582/
_version_ 1643826561586036736
score 13.211869

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