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The computation of zeros of Ahlfors map for doubly connected regions

The Ahlfors map and Szegö kernel are both classically related to each other. Ahlfors map can be computed using Szege kernel without relying on the zeros of Ahlfors map. The Szegö kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman­Stein kernel. The exact zeros of...

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Main Authors: Nazar, Kashif, Kareem Sangawi, Ali Wahab, Mohamed Murid, Ali Hassan, Yeak, Su Hoe
Format: Conference or Workshop Item
Published: AMERICAN INSTITUTE OF PHYSICS PUBLISING LLC 2016
Subjects:
Q Science
Online Access:http://eprints.utm.my/id/eprint/66952/
http://dx.doi.org/10.1063/1.4954520
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spelling my.utm.669522017-07-26T07:53:36Z http://eprints.utm.my/id/eprint/66952/ The computation of zeros of Ahlfors map for doubly connected regions Nazar, Kashif Kareem Sangawi, Ali Wahab Mohamed Murid, Ali Hassan Yeak, Su Hoe Q Science The Ahlfors map and Szegö kernel are both classically related to each other. Ahlfors map can be computed using Szege kernel without relying on the zeros of Ahlfors map. The Szegö kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman­Stein kernel. The exact zeros of the Ahlfors map are unknown except for the annulus region. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded doubly connected region. The method depends on the values of Szegö kernel, its derivative and the derivative of boundary correspondence function of Ahlfors map. Using combination of Nyström method, GMRES method, fast multiple method and Newton's method,the numerical examples presented here prove the effectiveness of the proposed method. AMERICAN INSTITUTE OF PHYSICS PUBLISING LLC 2016-01-06 Conference or Workshop Item PeerReviewed Nazar, Kashif and Kareem Sangawi, Ali Wahab and Mohamed Murid, Ali Hassan and Yeak, Su Hoe (2016) The computation of zeros of Ahlfors map for doubly connected regions. In: Aip Conference Proceedings, United States of America. http://dx.doi.org/10.1063/1.4954520
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/
topic Q Science
spellingShingle Q Science
Nazar, Kashif
Kareem Sangawi, Ali Wahab
Mohamed Murid, Ali Hassan
Yeak, Su Hoe
The computation of zeros of Ahlfors map for doubly connected regions
description The Ahlfors map and Szegö kernel are both classically related to each other. Ahlfors map can be computed using Szege kernel without relying on the zeros of Ahlfors map. The Szegö kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman­Stein kernel. The exact zeros of the Ahlfors map are unknown except for the annulus region. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded doubly connected region. The method depends on the values of Szegö kernel, its derivative and the derivative of boundary correspondence function of Ahlfors map. Using combination of Nyström method, GMRES method, fast multiple method and Newton's method,the numerical examples presented here prove the effectiveness of the proposed method.
format Conference or Workshop Item
author Nazar, Kashif
Kareem Sangawi, Ali Wahab
Mohamed Murid, Ali Hassan
Yeak, Su Hoe
author_facet Nazar, Kashif
Kareem Sangawi, Ali Wahab
Mohamed Murid, Ali Hassan
Yeak, Su Hoe
author_sort Nazar, Kashif
title The computation of zeros of Ahlfors map for doubly connected regions
title_short The computation of zeros of Ahlfors map for doubly connected regions
title_full The computation of zeros of Ahlfors map for doubly connected regions
title_fullStr The computation of zeros of Ahlfors map for doubly connected regions
title_full_unstemmed The computation of zeros of Ahlfors map for doubly connected regions
title_sort computation of zeros of ahlfors map for doubly connected regions
publisher AMERICAN INSTITUTE OF PHYSICS PUBLISING LLC
publishDate 2016
url http://eprints.utm.my/id/eprint/66952/
http://dx.doi.org/10.1063/1.4954520
_version_ 1643655866672480256
score 13.211869

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