N. Papamichael

TL;DR: A survey of the available numerical methods for approximating the conformal map can be found in this article, where the authors also illustrate the practical significance of the map by presenting a number of applications involving the solution of Laplacian boundary value problems.

TL;DR: In this paper, a numerical method based on the integral equation formulation of Symm is described for computing approximations to the mapping functions which accomplish the following conformal maps: (a) the mapping of a domain interior to a closed Jordan curve onto the interior of the unit disc, (b) mapping of an exterior domain exterior to closed Jordan curves onto the exterior of a unit disc.

TL;DR: In this paper, a cubic spline method is described for the numerical solution of a two-point boundary value problem involving a fourth order linear differential equation, which is closely related to a known fourth order finite difference scheme.

TL;DR: In this article, the stability and convergence properties of Bergman kernel methods for the numerical conformal mapping of simply and doubly connected domains are studied. But the authors focus on the stability of the results of Carleman kernels.