Nasser, Mohamed M. S. and Mohamed Murid, Ali Hassan and Sangawi, Ali W. K.
(2014)
*Numerical conformal mapping via a boundary integral equation with the adjoint generalized Neumann kernel.*
Twms Journal of Pure and Applied Mathematics, 5
(1).
pp. 96-117.
ISSN 2076-2585

Full text not available from this repository.

Official URL: http://dx.doi.org/10.48550/arXiv.1308.3929

## Abstract

This paper presents a new uniquely solvable boundary integral equation for computing the conformal mapping, its derivative and its inverse from bounded multiply connected regions onto the five classical canonical slit regions. The integral equation is derived by reformulating the conformal mapping as an adjoint Riemann-Hilbert problem. From the adjoint Riemann-Hilbert problem, we derive a boundary integral equation with the adjoint generalized Neumann kernel for the derivative of the boundary correspondence function θ′. Only the right-hand side of the integral equation is different from a canonical region to another. The function θ′ is integrated to obtain the boundary correspondence function θ. The integration constants as well as the parameters of the canonical region are computed using the same uniquely solvable integral equation. A numerical example is presented to illustrate the accuracy of the proposed method.

Item Type: | Article |
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Uncontrolled Keywords: | numerical conformal mapping, multiply connected regions |

Subjects: | Q Science > QA Mathematics |

Divisions: | Science |

ID Code: | 59849 |

Deposited By: | Haliza Zainal |

Deposited On: | 23 Jan 2017 00:24 |

Last Modified: | 20 Apr 2022 23:50 |

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