A domain decomposition method for approximating the conformal modules of long quadrilaterals
This paper is concerned with the study of a domain decomposition method for approximating the conformal modules of long quadrilaterals. The method has been studied already by the authors [Constructive Approximation 7, 349-379 (1991; Zbl 0729.30009) and ``Computational methods in function theory'', Proc. Conf., Valparaiso/Chile 1989, Lect. Notes Math. 1435, 155-169 (1990; Zbl 0705.30007)] and also by \textit{D. Gaier} and \textit{W. K. Hayman} [Rend. Mat. Appl., VIII. Ser. 10, 809-834 (1990), and Constructive Approximation 7, No. 4, 453-467 (1991)], but only in connection with a special class of quadrilaterals, viz. quadrilaterals where: (a) the defining domain is bounded by two parallel straight lines and two Jordan arcs, and (b) the four specified boundary points are the four corners where the arcs meet the straight lines. In the present paper we extend the application of the method to a much wider class of quadrilaterals and for each new application, we derive an estimate of the error in the resulting approximation to the conformal module.
scientific article; zbMATH DE number 4215914
scientific article