On the comparison of two numerical methods for conformal mapping

Abstract

Let G be a simply connected domain in the t plane (t = x + iy), bounded by the three straight lines x = 0, y = 0, x = 1 and a Jordan arc with cartesian equation y = τ(x). Also, let g be the function which maps conformally a rectangle R onto G, so that the four corners of R are mapped onto those of G. In this paper we show that the method considered in 1982 by Challis & Burley for determining approximations to g is equivalent to a special case of the well-known method of Garrick for the mapping of doubly connected domains. Hence, by using results already available in the literature, we provide some theoretical justification for the method of Challis & Burley. © 1987 Oxford University Press.