Integral and differential equations for conformal mapping of bounded multiply connected regions onto a disk with circular slits

• Main Authors: Mohamed Murid, Ali Hassan, Kareem Sangawi, Ali W., Nasser, M. M. S.
• Format: Article
• Language: English
• Published: Penerbit UTM Press 2011
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/39926/1/AliHassan2011_IntegralandDifferentialEquationsforConformalMapping.pdf; http://eprints.utm.my/id/eprint/39926/; https://dx.doi.org/10.11113/mjfas.v7n1.203

Conformal mapping is a useful tool in science and engineering. On the other hand exact mapping functions are unknown except for some special regions. In this paper we present a new boundary integral equation with classical Neumann kernel associated to f f , where f is a conformal mapping of bounded multiply connected regions onto a disk with circular slit domain. This boundary integral equation is constructed from a boundary relationship satisfied by a function analytic on a multiply connected region. With f f known, one can then treat it as a differential equation for computing f.