The approximate conformal mapping of a disk onto domain with an acute angle
Abstract
The method of boundary curve reparametrization is applied to construction of the approximate analytical conformal mapping of the unit disk onto an arbitrary given finite domain with a boundary smooth at every point but fininte number of acute angle points. The method is based on both the Fredholm equation solution and spline-interpolation. This approach consists of approximate solution of a linear system with unknown Fourier coefficients and construction of correction splines. The approximate mapping function has the form of a Cauchy integral. The method presentation is supported by demonstration of some examples. This method is applicable to the case of multiply connected domains with boundary angle points.
Keywords
Cite
@article{arxiv.2307.03516,
title = {The approximate conformal mapping of a disk onto domain with an acute angle},
author = {Pyotr N. Ivanshin and Elena A. Shirokova},
journal= {arXiv preprint arXiv:2307.03516},
year = {2023}
}
Comments
Accepted for publication in IJACM 11.01.23