A Fast Method for Solving Certain Integral Equations of the First Kind with Application to Conformal Mappings

摘要

A fast iterative solution method for Fredholm integral equations of the first kind with a logarithmic kernel as principal part is described. The method is a Fourier-Galerkin method. Due to the singularity of the kernel, the linear system of simultaneous equations is block diagonal dominant and can be solved rapidly by an iterative method. Examples of the computation of conformal mappings of simply and multiply connected domains are presented.