A boundary integral equation for the exterior neumann problem on multiply connected region

This research determines solutions of the exterior Neumann problem in multiply connected regions by using the method of boundary integral equations. The method depends on reducing the boundary value problem in question to an integral equation on the boundary of the domain of the problem, and then so...

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Main Author:	Chye, Mei Sian
Format:	Thesis
Language:	English
Published:	2010
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/17939/7/ChyeMeiSianMFSA2010.pdf
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id	my-utm-ep.17939
record_format	uketd_dc
spelling	my-utm-ep.179392017-09-18T04:36:55Z A boundary integral equation for the exterior neumann problem on multiply connected region 2010 Chye, Mei Sian QA Mathematics This research determines solutions of the exterior Neumann problem in multiply connected regions by using the method of boundary integral equations. The method depends on reducing the boundary value problem in question to an integral equation on the boundary of the domain of the problem, and then solves this integral equation. Our approach in this research is to convert the exterior Neumann problem into the exterior Riemann-Hilbert problem. The exterior Riemann-Hilbert problem is then solved using a uniquely solvable Fredholm integral equation on the boundary of the region. The kernel of this integral equation is the Neumann kernel. Once this equation is solved, the auxiliary function and the solution of the exterior Neumann problem can be obtained. As an examination of the proposed method, some numerical examples for some different test regions are presented. These examples include comparison between the numerical results and the exact solutions. Numerical examples reveal that the present method offers an effective solution technique for the exterior Riemann-Hilbert problems when the boundaries are sufficiently smooth. 2010 Thesis http://eprints.utm.my/id/eprint/17939/ http://eprints.utm.my/id/eprint/17939/7/ChyeMeiSianMFSA2010.pdf application/pdf en public masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Chye, Mei Sian A boundary integral equation for the exterior neumann problem on multiply connected region
description	This research determines solutions of the exterior Neumann problem in multiply connected regions by using the method of boundary integral equations. The method depends on reducing the boundary value problem in question to an integral equation on the boundary of the domain of the problem, and then solves this integral equation. Our approach in this research is to convert the exterior Neumann problem into the exterior Riemann-Hilbert problem. The exterior Riemann-Hilbert problem is then solved using a uniquely solvable Fredholm integral equation on the boundary of the region. The kernel of this integral equation is the Neumann kernel. Once this equation is solved, the auxiliary function and the solution of the exterior Neumann problem can be obtained. As an examination of the proposed method, some numerical examples for some different test regions are presented. These examples include comparison between the numerical results and the exact solutions. Numerical examples reveal that the present method offers an effective solution technique for the exterior Riemann-Hilbert problems when the boundaries are sufficiently smooth.
format	Thesis
qualification_level	Master's degree
author	Chye, Mei Sian
author_facet	Chye, Mei Sian
author_sort	Chye, Mei Sian
title	A boundary integral equation for the exterior neumann problem on multiply connected region
title_short	A boundary integral equation for the exterior neumann problem on multiply connected region
title_full	A boundary integral equation for the exterior neumann problem on multiply connected region
title_fullStr	A boundary integral equation for the exterior neumann problem on multiply connected region
title_full_unstemmed	A boundary integral equation for the exterior neumann problem on multiply connected region
title_sort	boundary integral equation for the exterior neumann problem on multiply connected region
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2010
url	http://eprints.utm.my/id/eprint/17939/7/ChyeMeiSianMFSA2010.pdf
_version_	1747815153681825792

A boundary integral equation for the exterior neumann problem on multiply connected region

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