A reparameterisation method to determine conformal maps
A conformal mapping of a simply connected Jordan region G onto the unit disk is constructed by computing the boundary correspondence. For this purpose the author uses the Symn integral equation as the main tool for his construction. The new idea in this paper is to construct a sufficiently smooth boundary representation of the given region by using a theorem of \textit{R. S. Lehman} [Pac. J. Math. 7, 1437-1449 (1957; Zbl 0087.289)]. The boundary representation is piecewise between occurring corners of the boundary. The method is applied to various test examples in which the given region is a circular sector where the opening angles are \(\frac{\pi}{2}\) and \(\frac{3\pi}{2}\). The examples show that in order to obtain high precision one has to take over hundred parameters into account.
scientific article; zbMATH DE number 3939649