Let R be a simply connected, nearly circular, starlike region containing the origin, D the unit disk and \(\phi\) : \(D\to R\) the conformal mapping normalized by \(\phi (0)=0\), \(\phi '(0)>0\). Under certain smoothness assumption of the boundary \(\partial R\) one may assume that \(\phi\) can be continuously extended onto the boundary \(\partial D\) of D. The boundary correspondence between \(\partial D\) and \(\partial R\) is then governed by Theodorsen’s integral equation which is the foundation of various numerical techniques to find \(\phi\) approximately.
The author investigates several methods including own ones and a method due to Hübner with respect to the observed (rather than theoretically predicted) convergence speed. He explains why these methods behave only linearly in convergence speed though by theoretical reasoning (locally) quadratic convergence could be expected. It is shown that the speed is eventually the speed of Wittich’s approximation for the conjugation operator.