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Solving third-order boundary value problem by direct methods

In this research, the direct method of multistep method is developed for the numerical solution of nonlinear boundary value problems (BVPs) of Type 1 and Type 2 directly. Most of the existing research involving BVPs will reduce the problem to a system of first order Ordinary Differential Equations...

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Main Author: Ahmad Zulkifli, Ahmad Shah Abdullah
Format: Thesis
Language:English
Published: 2014
Online Access:http://psasir.upm.edu.my/id/eprint/38487/1/IPM%202014%202%20IR.pdf
http://psasir.upm.edu.my/id/eprint/38487/
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spelling my.upm.eprints.384872017-01-13T08:16:55Z http://psasir.upm.edu.my/id/eprint/38487/ Solving third-order boundary value problem by direct methods Ahmad Zulkifli, Ahmad Shah Abdullah In this research, the direct method of multistep method is developed for the numerical solution of nonlinear boundary value problems (BVPs) of Type 1 and Type 2 directly. Most of the existing research involving BVPs will reduce the problem to a system of first order Ordinary Differential Equations (ODEs). However, the proposed method will solve the third-order BVPs directly without reducing to first-order ODEs with constant step size using the shooting technique. On- point and two-point direct block method of Adam Moulton have been derived. These methods consists the predictor and corrector method where the predictor is one order less than the corrector. In the numerical results, one-point direct methods have advantages in accuracy and for two-point direct block methods have advantages in timing calculation. The results clearly show that the proposed method is suitable for solving third-order nonlinear BVPs. 2014-02 Thesis NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/38487/1/IPM%202014%202%20IR.pdf Ahmad Zulkifli, Ahmad Shah Abdullah (2014) Solving third-order boundary value problem by direct methods. Masters thesis, Universiti Putra Malaysia.
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 In this research, the direct method of multistep method is developed for the numerical solution of nonlinear boundary value problems (BVPs) of Type 1 and Type 2 directly. Most of the existing research involving BVPs will reduce the problem to a system of first order Ordinary Differential Equations (ODEs). However, the proposed method will solve the third-order BVPs directly without reducing to first-order ODEs with constant step size using the shooting technique. On- point and two-point direct block method of Adam Moulton have been derived. These methods consists the predictor and corrector method where the predictor is one order less than the corrector. In the numerical results, one-point direct methods have advantages in accuracy and for two-point direct block methods have advantages in timing calculation. The results clearly show that the proposed method is suitable for solving third-order nonlinear BVPs.
format Thesis
author Ahmad Zulkifli, Ahmad Shah Abdullah
spellingShingle Ahmad Zulkifli, Ahmad Shah Abdullah
Solving third-order boundary value problem by direct methods
author_facet Ahmad Zulkifli, Ahmad Shah Abdullah
author_sort Ahmad Zulkifli, Ahmad Shah Abdullah
title Solving third-order boundary value problem by direct methods
title_short Solving third-order boundary value problem by direct methods
title_full Solving third-order boundary value problem by direct methods
title_fullStr Solving third-order boundary value problem by direct methods
title_full_unstemmed Solving third-order boundary value problem by direct methods
title_sort solving third-order boundary value problem by direct methods
publishDate 2014
url http://psasir.upm.edu.my/id/eprint/38487/1/IPM%202014%202%20IR.pdf
http://psasir.upm.edu.my/id/eprint/38487/
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score 13.211869

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