Error Analysis of the Bergman Kernel Method with Singular Basis Functions
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- 作者：Michalis A. Lytrides (1)
Nikos S. Stylianopoulos (1) - 关键词：numerical conformal mapping ; Bergman kernel method ; singular basis function ; 30C30 ; 30E10 ; 30C40 ; 65E05
- 刊名：Computational Methods and Function Theory
- 出版年：2012
- 出版时间：January 2012
- 年：2012
- 卷：11
- 期：2
- 页码：487-526
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Nikos S. Stylianopoulos (1)
1. Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678, Nicosia, Cyprus - ISSN：2195-3724
文摘
Let G be a bounded Jordan domain in the complex plane with a piecewise analytic boundary. We present theoretical estimates and numerical evidence for certain phenomena, regarding the application of the Bergman kernel method with algebraic and pole singular basis functions, for approximating the conformal mapping of G onto the normalized disk. Thereby, we complete the task of providing full theoretical justification of this method.