An integral equation method for solving exterior Neumann problems on smooth regions

This work develops a boundary integral equation method for numerical solution of the exterior Neumann problem. An integral equation for solving the exterior Neumann problem in a simply connected region is derived in this dissertation based on the exterior Riemann-Hilbert problem. In the first step t...

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Main Author:	Jumadi, Azlina
Format:	Thesis
Language:	English
Published:	2009
Subjects:	Q Science (General) QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/12322/6/AzlinaJumadiMFS2009.pdf
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id	my-utm-ep.12322
record_format	uketd_dc
spelling	my-utm-ep.123222017-09-17T05:37:33Z An integral equation method for solving exterior Neumann problems on smooth regions 2009-11 Jumadi, Azlina Q Science (General) QA Mathematics This work develops a boundary integral equation method for numerical solution of the exterior Neumann problem. An integral equation for solving the exterior Neumann problem in a simply connected region is derived in this dissertation based on the exterior Riemann-Hilbert problem. In the first step the exterior Neumann problem is reduced to an exterior Riemann-Hilbert problem for the derivative of an auxiliary function which is analytic in the region. Then, the exterior Riemann-Hilbert problem is transformed to a uniquely solvable Fredholm integral equation on the boundary of the region. Once this equation is solved, the auxiliary function and the solution of the exterior Neumann problem can be obtained. The efficiency of the method is illustrated by some numerical examples. 2009-11 Thesis http://eprints.utm.my/id/eprint/12322/ http://eprints.utm.my/id/eprint/12322/6/AzlinaJumadiMFS2009.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	Q Science (General) QA Mathematics
spellingShingle	Q Science (General) QA Mathematics Jumadi, Azlina An integral equation method for solving exterior Neumann problems on smooth regions
description	This work develops a boundary integral equation method for numerical solution of the exterior Neumann problem. An integral equation for solving the exterior Neumann problem in a simply connected region is derived in this dissertation based on the exterior Riemann-Hilbert problem. In the first step the exterior Neumann problem is reduced to an exterior Riemann-Hilbert problem for the derivative of an auxiliary function which is analytic in the region. Then, the exterior Riemann-Hilbert problem is transformed to a uniquely solvable Fredholm integral equation on the boundary of the region. Once this equation is solved, the auxiliary function and the solution of the exterior Neumann problem can be obtained. The efficiency of the method is illustrated by some numerical examples.
format	Thesis
qualification_level	Master's degree
author	Jumadi, Azlina
author_facet	Jumadi, Azlina
author_sort	Jumadi, Azlina
title	An integral equation method for solving exterior Neumann problems on smooth regions
title_short	An integral equation method for solving exterior Neumann problems on smooth regions
title_full	An integral equation method for solving exterior Neumann problems on smooth regions
title_fullStr	An integral equation method for solving exterior Neumann problems on smooth regions
title_full_unstemmed	An integral equation method for solving exterior Neumann problems on smooth regions
title_sort	integral equation method for solving exterior neumann problems on smooth regions
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2009
url	http://eprints.utm.my/id/eprint/12322/6/AzlinaJumadiMFS2009.pdf
_version_	1747814923139809280

An integral equation method for solving exterior Neumann problems on smooth regions

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