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2014•Russian MathematicsRequires access

On the approximate conformal mapping of the unit disk on a simply connected domain

Elena A. Shirokova

Open publisher page 16 citations

Abstract

We present a method of constructing the analytic function realizing an approximate conformal mapping of the unit disk on an arbitrary simply connected domain with the given smooth parametrically defined boundary. The method is based on a new boundary parameterization. Solution of the problem is reduced to the Fredholm integral equation of the second kind. We present the examples of three ways to solve the integral equation.

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What this paper is about

We present a method of constructing the analytic function realizing an approximate conformal mapping of the unit disk on an arbitrary simply connected domain with the given smooth parametrically defined boundary. The method is based on a new boundary parameterization. Solution of the problem is reduced to the Fredholm integral equation of the second kind. We present the examples of three ways to solve the integral equation.

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OpenAlex reports 16 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We present a method of constructing the analytic function realizing an approximate conformal mapping of the unit disk on an arbitrary simply connected domain with the given smooth parametrically defined boundary. The method is based on a new boundary parameterization. Solution of the problem is reduced to the Fredholm integral equation of the second kind. We present the examples of three ways to solve the integral equation.

Key concepts: Unit disk, Conformal map, Mathematics, Simply connected space, Boundary (topology), Domain (mathematical analysis), Mathematical analysis, Fredholm integral equation

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