A fast method for solving certain integral equations of the first kind with application to conformal mapping

摘要

We describe a fast iterative method for solving Fredholm integral equations of the first kind whose kernels have a logarithmic principal part. The method is a Fourier—Galerkin method, and due to the singularity of the kernel, the linear system of simultaneous equations is block diagonally dominant and can be solved rapidly by an iterative method. We present examples of the computation of conformal mappings of simply and multiply connected domains.