NUMERICAL CONFORMAL MAPPING
FOR EXTERIOR REGIONS VIA THE
KERZMAN-STEIN KERNEL

A.H.M. MURID, M.Z. NASHED
AND M.R.M. RAZALI

Abstract:

A simple numerical method is described for computing a conformal map from a domain exterior to a smooth Jordan curve in the complex plane onto the exterior of the unit disk. The numerical method is based on a boundary integral equation similar to the Kerzman-Stein integral equation for interior mappings. Typical examples show that numerical results of high accuracy can be obtained provided that the boundaries are smooth.