A simplified Fornberg-like method for the conformal mapping of multiply connected regions—Comparisons and crowding

We present a new Fornberg-like method for the numerical conformal mapping of multiply connected regions exterior to circles to multiply connected regions exterior to smooth curves. The method is based on new, symmetric conditions for analytic extension of functions given on circular boundaries. We also briefly discuss a similar method due to Wegmann and compare some computations with both methods. Some examples of regions which exhibit crowding of the circles are also presented.