Integral equation approach for computing green's function on unbounded simply connected region

This research is to compute the Green’s function on an unbounded simply connected region by conformal mapping and by solving an exterior Dirichlet problem. The exact Green’s function is found by using Riemann mapping and M bius transform. The Dirichlet problem is then solved using a uniquely solvabl...

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Main Author:	Nezhad, Sheida Chahkandi
Format:	Thesis
Language:	English
Published:	2013
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/48222/1/SheidaChahkandiNezhadMFS2013.pdf
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id	my-utm-ep.48222
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spelling	my-utm-ep.482222017-09-17T08:33:30Z Integral equation approach for computing green's function on unbounded simply connected region 2013 Nezhad, Sheida Chahkandi QA Mathematics This research is to compute the Green’s function on an unbounded simply connected region by conformal mapping and by solving an exterior Dirichlet problem. The exact Green’s function is found by using Riemann mapping and M bius transform. The Dirichlet 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 generalized Neumann kernel. The method for solving this integral equation is by using the Nystr?m method with the trapezoidal rule to discretize it into a system. The linear system is solved by the Gaussian elimination method. As an examination of the proposed method, several numerical examples for some various test regions are presented. These examples include a comparison between the numerical result and the exact solutions 2013 Thesis http://eprints.utm.my/id/eprint/48222/ http://eprints.utm.my/id/eprint/48222/1/SheidaChahkandiNezhadMFS2013.pdf application/pdf en public http://libraryopac.utm.my/client/en_AU/main/search/results?qu=Integral+equation+approach+for+computing+green%27s+function+on+unbounded+simply+connected+region&te= 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 Nezhad, Sheida Chahkandi Integral equation approach for computing green's function on unbounded simply connected region
description	This research is to compute the Green’s function on an unbounded simply connected region by conformal mapping and by solving an exterior Dirichlet problem. The exact Green’s function is found by using Riemann mapping and M bius transform. The Dirichlet 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 generalized Neumann kernel. The method for solving this integral equation is by using the Nystr?m method with the trapezoidal rule to discretize it into a system. The linear system is solved by the Gaussian elimination method. As an examination of the proposed method, several numerical examples for some various test regions are presented. These examples include a comparison between the numerical result and the exact solutions
format	Thesis
qualification_level	Master's degree
author	Nezhad, Sheida Chahkandi
author_facet	Nezhad, Sheida Chahkandi
author_sort	Nezhad, Sheida Chahkandi
title	Integral equation approach for computing green's function on unbounded simply connected region
title_short	Integral equation approach for computing green's function on unbounded simply connected region
title_full	Integral equation approach for computing green's function on unbounded simply connected region
title_fullStr	Integral equation approach for computing green's function on unbounded simply connected region
title_full_unstemmed	Integral equation approach for computing green's function on unbounded simply connected region
title_sort	integral equation approach for computing green's function on unbounded simply connected region
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2013
url	http://eprints.utm.my/id/eprint/48222/1/SheidaChahkandiNezhadMFS2013.pdf
_version_	1747817337689473024

Integral equation approach for computing green's function on unbounded simply connected region

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