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Numerical experiment on conformal mapping of doubly connected regions onto a disk with a slit. (English) Zbl 1178.30004
The authors present a method for computing conformal mappings of ring-domains bounded by regular Jordan curves onto a disk |w|<r with a concentric circular slit |w|=μr, 0<μ<1. Starting from an integral boundary equation with the Neumann kernel they derive a system of integral equations. Then the system is solved numerically by the method of Nyström with the trapez rule. They provide five examples in which exact forms of the mapping are known.

MSC:
30C30Numerical methods in conformal mapping theory
65R20Integral equations (numerical methods)
65E05Numerical methods in complex analysis