On conformal mapping of a unit disk onto a finite domain (Q2709544)

Let \(z=\omega (\xi)\) be a conformal mapping of \(\mathbb{D}\) onto the interior \(G\) of a piecewise smooth Jordan curve \(S\). The authors consider the problem to approximate \(\omega\) by a polynomial \(\omega_n\) for which they take a section of the power series expansion of \(\omega\). To compute its Taylor coefficients, they use the inverse function \(f\) of \(\omega\), which is approximated by another method involving the solution of a Dirichlet problem. Two test examples, in which \(S\) are ellipses, are given. -- The method seems complicated and not useful when \(S\) has corners.