A STUDY ON THE EFFECTIVE ALGORITHMS BASED ON THE WEGMANN'S METHOD

Abstract

Determinations of conformal map from the unit disk onto a Jordan region are reduced to solve the Theodorsen equation which is an integral equation for the boundary correspondence function. Among numerical conformal maps the Wegmann's method is well known as a Newton efficient one for solving Theodorsen equation. However this method has not so wide class of convergence. We proposed as an improved method for convergence by applying a low frequency filter to the Wegmann's method. In this paper, we investigate error analysis and propose an automatic algorithm based on this analysis.

Keywords

• Conformal mapping;
• Wegmann's method;
• low frequency filter;
• error estimate;
• automatic algorithm