A numerical method for locating the zeros of ahlfors map for doubly connected regions

• Main Authors: Sangawi, Ali W. K., Nazar, Kashif, Murid, Ali Hassanmohamed
• Format: Conference or Workshop Item
• Published: 2015
• Subjects: QA75 Electronic computers. Computer science
• Online Access: http://eprints.utm.my/id/eprint/61627/; http://www.icsccm.com/2015/WB/
• Institution: Universiti Teknologi Malaysia

The Ahlfors map and Szeg¨o kernel are both classically related to each other. Ahlfors map can be computed using Szeg¨o kernel without relying on the zeros of Ahlfors map. The Szeg¨o kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman-Stein kernel. The exact zeros of the Ahlfors map are unknown except for the annulus region. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded doubly connected region. The method depends on the values of Szeg¨o kernel, its derivative and the derivative of boundary correspondence function of Ahlfors map. The numerical examples presented here prove the effectiveness of the proposed method.