w9260228 SUMMARYTwo numerical methods are considered for the conformal mapping of a bounded simply-connected domain onto the unit disc. The two methods are respectively the Bergman kernel method, which has been described in [17], and the so-called Ritz method.In this paper we indicate the close theoretical relationship of the two methods, compare their computational efficiencies and present a number of practical applications of the approximate conformal maps.

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w926004× SUMMARYThe work of the present paper is closely related to the two numerical procedures described in [11], for determining approximations to the function which maps conformally a bounded simply-connected domain Ω 1 , with boundary ∂Ω, onto the unit disc. Here, we consider the use of these procedures for the solution of the corresponding exterior problem, i.e. the problem of determining approximations to the mapping function which maps conformally the exterior domain Ω = compl(Ω I ⋃∂Ω) onto the unit disc.

This paper is concerned with the problem of determining approximations to the function F which maps conformally a simply-connected domain Ω onto a rectangle R, so that four specified points on are mapped Ω ∂

We consider the use of an orthonormalization method for constructing approximations to one of the standard conformal maps for multiply-connected domains. The method has been used successfully in [12], but only for the mapping of doubly-connected domains. Our purpose here is to consider its application to the mapping of domains whose connectivity is greater than two.