Nystrom method for solving non-uniquely solvable interior Riemann-Hilbert problem on region with corners via integral equation

This work involve a boundary integral equation method to find the non-uniquely solvable numerical solution of the Interior Riemann-Hilbert problem on a region with corners. The integral equation was derived based on the Fredholm integral equation of the second kind with continuous kernel and the sol...

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Main Author:	Hussein, Shwan Hassan
Format:	Thesis
Language:	English
Published:	2012
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/32346/1/ShwanHassanHusseinMFS2012.pdf
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id	my-utm-ep.32346
record_format	uketd_dc
spelling	my-utm-ep.323462017-09-20T05:53:09Z Nystrom method for solving non-uniquely solvable interior Riemann-Hilbert problem on region with corners via integral equation 2012-12 Hussein, Shwan Hassan QA Mathematics This work involve a boundary integral equation method to find the non-uniquely solvable numerical solution of the Interior Riemann-Hilbert problem on a region with corners. The integral equation was derived based on the Fredholm integral equation of the second kind with continuous kernel and the solvability of the integral equation and its equivalence to the problem is reviewed the derived integral equation in this research for the non-uniquely solvable interior Riemann-Hilbert problem on a region with corners will be computed in achieving this aim, this study developed two numerical formulas where the Nystrom method with the Gaussian quadrature rule are implemented. So that, the singularities are eliminated during numerical integration. Numerical examples on four test regions with 0ff-corners are presented to demonstrate the effectiveness of this formulation. 2012-12 Thesis http://eprints.utm.my/id/eprint/32346/ http://eprints.utm.my/id/eprint/32346/1/ShwanHassanHusseinMFS2012.pdf application/pdf en public masters Universiti Teknologi Malaysia, Faculty of Chemical Engineering Faculty of Chemical Engineering
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Hussein, Shwan Hassan Nystrom method for solving non-uniquely solvable interior Riemann-Hilbert problem on region with corners via integral equation
description	This work involve a boundary integral equation method to find the non-uniquely solvable numerical solution of the Interior Riemann-Hilbert problem on a region with corners. The integral equation was derived based on the Fredholm integral equation of the second kind with continuous kernel and the solvability of the integral equation and its equivalence to the problem is reviewed the derived integral equation in this research for the non-uniquely solvable interior Riemann-Hilbert problem on a region with corners will be computed in achieving this aim, this study developed two numerical formulas where the Nystrom method with the Gaussian quadrature rule are implemented. So that, the singularities are eliminated during numerical integration. Numerical examples on four test regions with 0ff-corners are presented to demonstrate the effectiveness of this formulation.
format	Thesis
qualification_level	Master's degree
author	Hussein, Shwan Hassan
author_facet	Hussein, Shwan Hassan
author_sort	Hussein, Shwan Hassan
title	Nystrom method for solving non-uniquely solvable interior Riemann-Hilbert problem on region with corners via integral equation
title_short	Nystrom method for solving non-uniquely solvable interior Riemann-Hilbert problem on region with corners via integral equation
title_full	Nystrom method for solving non-uniquely solvable interior Riemann-Hilbert problem on region with corners via integral equation
title_fullStr	Nystrom method for solving non-uniquely solvable interior Riemann-Hilbert problem on region with corners via integral equation
title_full_unstemmed	Nystrom method for solving non-uniquely solvable interior Riemann-Hilbert problem on region with corners via integral equation
title_sort	nystrom method for solving non-uniquely solvable interior riemann-hilbert problem on region with corners via integral equation
granting_institution	Universiti Teknologi Malaysia, Faculty of Chemical Engineering
granting_department	Faculty of Chemical Engineering
publishDate	2012
url	http://eprints.utm.my/id/eprint/32346/1/ShwanHassanHusseinMFS2012.pdf
_version_	1747815980609830912

Nystrom method for solving non-uniquely solvable interior Riemann-Hilbert problem on region with corners via integral equation

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