Mohamed Murid, Ali Hassan and Mohamed, Nurul Akmal
(2007)
*Numerical conformal mapping of doubly connected regions using integral equation via the Kerzman-Stein kernel and Cauchy's integral formula.*
In: Proceedings of Simposium Kebangsaan Sains Matematik ke-15, 2007, UiTM Shah Alam.

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## Abstract

An integral equation method based on the Kerzman-Stein kernelfor conformal mapping of smooth doubly connected regions onto an annulus A = { w : µ < | w | < 1 } is presented. The theoretical development is basedon the boundary integral equation for conformal mapping of doubly connectedregions with Kerzman-Stein kernel derived by Razali and one of the authors [8].However, the integral equation is not in the form of Fredholm integral equationand no numerical experiments are reported. In this paper, we show that usingthe boundary relationship satisﬁed by a function analytic in a doubly connectedregion, then the previous integral equation can be reduced to a numericallytractable integral equation which however involves the unknown inner radius, µ . For numerical experiments, we discretized the integral equation which leadsto an over determined system of non-linear equations. The system obtained issolved simultaneously using Gauss-Newton method and Lavenberg-Marquardtwith Fletcher’s algorithm for solving the non-linear least squares problems.Numerical implementations on some test regions are also presented.

Item Type: | Conference or Workshop Item (Paper) |
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Uncontrolled Keywords: | Numerical conformal mapping, integral equation, Kerzman-Stein kernel and Cauchy's integral formula |

Subjects: | Q Science > Q Science (General) |

Divisions: | Science |

ID Code: | 14246 |

Deposited By: | Mrs Liza Porijo |

Deposited On: | 23 Aug 2011 05:53 |

Last Modified: | 08 Aug 2017 02:57 |

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