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An integral equation related to the exterior riemann-hilbert problem on region with corners

Nasser in 2005 gives the first full method for solving the Riemann-Hilbert problem (briefly the RH problem) for smooth arbitrary simply connected region for general indices via boundary integral equation. However, his treatment of RH problem does not include regions with corners. Later, Ismail in 20...

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Main Authors: Zamzamir, Zamzana, Ismail, Munira, Mohamed Murid, Ali Hassan
Format: Article
Language:English
Published: Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia 2008
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/7102/1/MuniraIsmail2008_AnIntegralEquationRelated.pdf
http://eprints.utm.my/id/eprint/7102/
http://jfs.ibnusina.utm.my/index.php/jfs/issue/view/22/showToc
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spelling my.utm.71022017-10-22T07:56:22Z http://eprints.utm.my/id/eprint/7102/ An integral equation related to the exterior riemann-hilbert problem on region with corners Zamzamir, Zamzana Ismail, Munira Mohamed Murid, Ali Hassan QA Mathematics Nasser in 2005 gives the first full method for solving the Riemann-Hilbert problem (briefly the RH problem) for smooth arbitrary simply connected region for general indices via boundary integral equation. However, his treatment of RH problem does not include regions with corners. Later, Ismail in 2007 provides a numerical solution of the interior RH problem on region with corners via Nasser’s method together with Swarztrauber’s approach, but Ismail does not develop any integral equation related to exterior RH problem on region with corners. In this paper, we introduce a new integral equation related to the exterior RH problem in a simply connected region bounded by curves having a finite number of corners in the complex plane. We obtain a new integral equation that adopts Ismail’s method which does not involve conformal mapping. This result is a generalization of the integral equation developed by Nasser for the exterior RH problem on smooth region. The solvability of the integral equation in accordance with the Fredholm alternative theorem is presented. The proof of the equivalence of our integral equation to the RH problem is also provided Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia 2008 Article PeerReviewed application/pdf en http://eprints.utm.my/id/eprint/7102/1/MuniraIsmail2008_AnIntegralEquationRelated.pdf Zamzamir, Zamzana and Ismail, Munira and Mohamed Murid, Ali Hassan (2008) An integral equation related to the exterior riemann-hilbert problem on region with corners. Journal of Fundamental Sciences, 4 (2). pp. 369-377. ISSN 1823-626X http://jfs.ibnusina.utm.my/index.php/jfs/issue/view/22/showToc
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Zamzamir, Zamzana
Ismail, Munira
Mohamed Murid, Ali Hassan
An integral equation related to the exterior riemann-hilbert problem on region with corners
description Nasser in 2005 gives the first full method for solving the Riemann-Hilbert problem (briefly the RH problem) for smooth arbitrary simply connected region for general indices via boundary integral equation. However, his treatment of RH problem does not include regions with corners. Later, Ismail in 2007 provides a numerical solution of the interior RH problem on region with corners via Nasser’s method together with Swarztrauber’s approach, but Ismail does not develop any integral equation related to exterior RH problem on region with corners. In this paper, we introduce a new integral equation related to the exterior RH problem in a simply connected region bounded by curves having a finite number of corners in the complex plane. We obtain a new integral equation that adopts Ismail’s method which does not involve conformal mapping. This result is a generalization of the integral equation developed by Nasser for the exterior RH problem on smooth region. The solvability of the integral equation in accordance with the Fredholm alternative theorem is presented. The proof of the equivalence of our integral equation to the RH problem is also provided
format Article
author Zamzamir, Zamzana
Ismail, Munira
Mohamed Murid, Ali Hassan
author_facet Zamzamir, Zamzana
Ismail, Munira
Mohamed Murid, Ali Hassan
author_sort Zamzamir, Zamzana
title An integral equation related to the exterior riemann-hilbert problem on region with corners
title_short An integral equation related to the exterior riemann-hilbert problem on region with corners
title_full An integral equation related to the exterior riemann-hilbert problem on region with corners
title_fullStr An integral equation related to the exterior riemann-hilbert problem on region with corners
title_full_unstemmed An integral equation related to the exterior riemann-hilbert problem on region with corners
title_sort integral equation related to the exterior riemann-hilbert problem on region with corners
publisher Ibnu Sina Institute for Fundamental Science Studies, Universiti Teknologi Malaysia
publishDate 2008
url http://eprints.utm.my/id/eprint/7102/1/MuniraIsmail2008_AnIntegralEquationRelated.pdf
http://eprints.utm.my/id/eprint/7102/
http://jfs.ibnusina.utm.my/index.php/jfs/issue/view/22/showToc
_version_ 1643644702970347520
score 13.251813

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