Kress smoothing transformation for weakly singular Fredholm integral equation of second kind

This work investigates a numerical method for the second kind Fredholm integral equation with weakly singular kernel k(x, y), in particular, when k(x, y) = ln |x-y|, and k(x, y) = |x-y|-a, -1 = x, y = 1, 0 < a < 1. The solutions of such equations may exhibit a singular behaviour in the neighbo...

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Main Author:	Mohamed Saeed Bawazir, Hassan
Format:	Thesis
Language:	English
Published:	2006
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/5302/10/HassanMohamedSaeedBawazirMFS2006.pdf
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id	my-utm-ep.5302
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spelling	my-utm-ep.53022017-10-12T04:43:55Z Kress smoothing transformation for weakly singular Fredholm integral equation of second kind 2006-03 Mohamed Saeed Bawazir, Hassan QA Mathematics This work investigates a numerical method for the second kind Fredholm integral equation with weakly singular kernel k(x, y), in particular, when k(x, y) = ln \|x-y\|, and k(x, y) = \|x-y\|-a, -1 = x, y = 1, 0 < a < 1. The solutions of such equations may exhibit a singular behaviour in the neighbourhood of the endpoints x = Â±1. We introduce a new smoothing transformation based on the Kress transformation for solving weakly singular Fredholm integral equations of the second kind, and then using the Hermite smoothing transformation as a standard. With the transformation an equation which is still weakly singular is obtained, but whose solution is smoother. The transformed equation is then solved numerically by product integration methods with interpolating polynomials. Two types of interpolating polynomials, namely the Gauss-Legendre and Chebyshev polynomials, have been used. Numerical examples are presented to investigate the performance of the former. 2006-03 Thesis http://eprints.utm.my/id/eprint/5302/ http://eprints.utm.my/id/eprint/5302/10/HassanMohamedSaeedBawazirMFS2006.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 Mohamed Saeed Bawazir, Hassan Kress smoothing transformation for weakly singular Fredholm integral equation of second kind
description	This work investigates a numerical method for the second kind Fredholm integral equation with weakly singular kernel k(x, y), in particular, when k(x, y) = ln \|x-y\|, and k(x, y) = \|x-y\|-a, -1 = x, y = 1, 0 < a < 1. The solutions of such equations may exhibit a singular behaviour in the neighbourhood of the endpoints x = Â±1. We introduce a new smoothing transformation based on the Kress transformation for solving weakly singular Fredholm integral equations of the second kind, and then using the Hermite smoothing transformation as a standard. With the transformation an equation which is still weakly singular is obtained, but whose solution is smoother. The transformed equation is then solved numerically by product integration methods with interpolating polynomials. Two types of interpolating polynomials, namely the Gauss-Legendre and Chebyshev polynomials, have been used. Numerical examples are presented to investigate the performance of the former.
format	Thesis
qualification_level	Master's degree
author	Mohamed Saeed Bawazir, Hassan
author_facet	Mohamed Saeed Bawazir, Hassan
author_sort	Mohamed Saeed Bawazir, Hassan
title	Kress smoothing transformation for weakly singular Fredholm integral equation of second kind
title_short	Kress smoothing transformation for weakly singular Fredholm integral equation of second kind
title_full	Kress smoothing transformation for weakly singular Fredholm integral equation of second kind
title_fullStr	Kress smoothing transformation for weakly singular Fredholm integral equation of second kind
title_full_unstemmed	Kress smoothing transformation for weakly singular Fredholm integral equation of second kind
title_sort	kress smoothing transformation for weakly singular fredholm integral equation of second kind
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2006
url	http://eprints.utm.my/id/eprint/5302/10/HassanMohamedSaeedBawazirMFS2006.pdf
_version_	1747814574667595776

Kress smoothing transformation for weakly singular Fredholm integral equation of second kind

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