Error Analysis of the Bergman Kernel Method with Singular Basis Functions

Abstract

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.

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Correspondence to Michalis A. Lytrides.

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Lytrides, M.A., Stylianopoulos, N.S. Error Analysis of the Bergman Kernel Method with Singular Basis Functions. Comput. Methods Funct. Theory 11, 487–526 (2012). https://doi.org/10.1007/BF03321873

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En]Keywords

  • numerical conformal mapping
  • Bergman kernel method
  • singular basis function

2000 MSC

  • 30C30
  • 30E10
  • 30C40
  • 65E05