Numerical Conformal Mappings onto the Canonical Slit Domains Listed in Koebe (1916)

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Conformal mappings are familiar in science and engineering. Using the charge simulation method, we proposed a unified method of numerical conformal mappings of unbounded multiply connected domains onto the linear and the spiral slit canonical domains, where oblique angles of the slits were individually specified, and showed its effectiveness by numerical experiments. The method is applicable also to the problem of bounded domains in principle. As a result, approximate mapping functions onto the first thirteen of the thirty nine canonical slit domains listed in Koebe (1916) are obtainable in a more general form as described above.