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Zbl 1198.30009
Nasser, Mohamed M.S.
Numerical conformal mapping via a boundary integral equation with the generalized Neumann kernel. (English)
[J] SIAM J. Sci. Comput. 31, No. 3, 1695-1715 (2009). ISSN 1064-8275; ISSN 1095-7197/e

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.
[H. P. Dikshit (Bhopal)]

MSC 2000:: *30C30 Numerical methods in conformal mapping theory
30E25 Boundary value problems, complex analysis
65E05 Numerical methods in complex analysis

Keywords: numerical conformal mapping; multiply connected regions; generalized Neumann kernel

Citations: Zbl 1159.30007; Zbl 0040.19001; Zbl 0208.34302; Zbl 0473.30006

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