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Numerical conformal mapping via a boundary integral equation with the generalized Neumann kernel. (English) Zbl 1198.30009
The main object of the paper is to present a unified boundary integral method for numerical conformal mappings of bounded (see [{\it M. M. S. Nasser}, Comput. Methods Funct. Theory 9, No. 1, 127--143 (2009; Zbl 1159.30007)]) and unbounded (see, e.g., [{\it S. Bergman}, The kernel function and conformal mapping, Mathematical Surveys. 5. Providence, R.I.: American Mathematical Society (AMS) (1950; Zbl 0040.19001) (1970; Zbl 0208.34302) (1980; Zbl 0473.30006)]) multiply connected regions onto the five classical canonical slit domains, Using this method, the approximate parameters and mapping functions onto the five canonical slit domains can be computed by solving a linear systems with a common coefficient matrix. Several numerical examples are also given to support the effectiveness of the method.

30C30Numerical methods in conformal mapping theory
30E25Boundary value problems, complex analysis
65E05Numerical methods in complex analysis
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