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Numerical conformal mapping via the Bergman kernel using Fourier method

Teh, Yuan Ying (2006) Numerical conformal mapping via the Bergman kernel using Fourier method. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science.

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Abstract

The Szego kernel and the Bergman kernel of a simply connected region in the complex plane are kernel functions which are related to the Riemann mapping function. An effcient method based on the Kerzman-Stein-Trummer integral equation for computing the Szego kernel has been known since 1986. In 1997, integral equation for the Bergman kernel which can be used effectively for numerical conformal mapping has also been established. Both of these integral equations have been solved by means of Nystrom’s method. Our subject of study is based on integral equation for Bergman kernel, where we had solved this integral equation by means of Fourier method. Since integral equation for Bergman kernel has not yet been solved using Fourier method, the numerical results can also be used to compare with those obtained from Nystrom’s method. As a result, Fourier method is capable to produce approximations of comparable accuracy to the Nystrom’s method; where these approximations are also suitable for numerical conformal mapping.

Item Type:Thesis (Masters)
Additional Information:Thesis (Master of Science (Mathematics)) - Universiti Teknologi Malaysia, 2006; Supervisor : Assoc. Prof. Dr. Ali Hassan Mohamed Murid
Uncontrolled Keywords:Complex plane; kernel functions; Szego kernel; Bergman kernel; numerical conformal mapping; integral equation
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:3725
Deposited By: Ms Zalinda Shuratman
Deposited On:21 Jun 2007 07:46
Last Modified:09 Jul 2012 03:47

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