Title: New method of computing the Riemann mapping function via real valued kerne

Abstract

A new boundary integral equation to compute the Riemann mapping function for bounded simply connected regions corresponding to a real valued kernel is presented. Based on the multiplication of the Kerzman-Stien Trummer integral equation (KST) by the penalty function such that the complex-valued kernel is transformed into a real-valued kernel, we derive a new boundary integral equation and prove its uniqueness. Numerical results using the Nystrom method with the trapezoidal rule yield approximations of high accuracy when compared with exact solutions for test regions.