Abstract
In this paper, we study numerical conformal mappings of ring domains with the charge simulation method. The method has been applied to solve a lot of problems in electrical engineering. This paper is devoted to giving numerical results by new algorithms based on potentially theoretical considerations for the charge simulation method of numerical conformal mappings in ring domains.
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References
L.V. Ahlfors, Complex Analysis. 2nd ed., McGraw-Hill, New York, 1966.
K. Amano, A charge simulation method for the numerical conformal mapping of interior, exterior and doubly-connected domains. J. Comput. Appl. Math.,53 (1994), 353–370.
K. Amano, A bidirectional method for numerical conformal mapping based on the charge simulation method. J. Inform. Process.,14 (1991), 473–482.
K. Amano, Numerical conformal mapping onto the circular slit domains (in Japanese). Trans. Inform. Process. Soc. Japan,36 (1995), 219–225.
D. Gaier, Lecture on Complex Approximation. Birkhäuser, 1987.
T. Inoue, A remark on zeros of weighted Chebyshev polynomials. Appl. Math. Lett.,4 (1991), 63–65.
T. Inoue, Asymptotic behavior of extremal weighted polynomials. Mathématica, L’Acad. Répub. Soc. Rouman,35(58) (1993), 29–34.
T. Inoue, Some properties of weighted hyperbolic polynomials. Internat. J. Math. Math. Sci.,19 (1996), 9–14.
T. Inoue, Applications of asymptotic theorem on weighted extremal polynomials. Trans. Japan Indust. Appl. Math.,4 (1994), 205–209.
M. Katsurada and H. Okamoto, On the collocation points of the fundamental solution method for the potential problem. Comput. Math. Appl.,31 (1996), 123–137.
N.S. Landkof, Foundation of Modern Potential Theory. Springer, 1972.
H.N. Mhaskar and E.B. Saff, Where does the sup norm of a weighted polynomial live? Constr. Approx.,1 (1985), 71–91.
H.N. Mhaskar and E.B. Saff, Weighted analogues of capacity, transfinite diameter and Chebyshev constant. Constr. Approx.,8 (1992), 105–124.
K. Murota, Comparison of conventional and invariant schemes of fundamental solutions method for annular domains. Japan J. Indust. Appl. Math.,12 (1995), 61–85.
K. Nishida, Mathematical and numerical analysis of charge simulation method in 2-dimensional elliptic domains. Trans. Japan Indust. Appl. Math.,5 (1995), 185–198.
E. Song, H. Sugiura and T. Sakurai, Analysis of instability and Wegmann’s method for conformal mapping. Trans. Inform. Process. Soc. Japan,32 (1991), 126–132.
M. Sugihara, Approximations of harmonic functions (in Japanese). Kokyuroku 676, Res. Inst. Math. Sci. Kyouto Univ., 1988, 251–261.
H. Sugiura and T. Torii, A method for constructing generalized Runge-Kutta methods. J. Comput. Appl. Math.,38 (1991), 399–410.
M. Tsuji, Potential Theory in Modern Function Theory. 2nd ed., Chelsea, New York, 1958.
S. Yotsutani, The suitable distribution of charge points (in Japanese). Kokyuroku 703, Res. Inst. Math. Sci. Kyouto Univ., 1989, 172–186.
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Inoue, T. New charge simulation method for numerical conformal mapping of ring domains. Japan J. Indust. Appl. Math. 14, 295–301 (1997). https://doi.org/10.1007/BF03167269
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DOI: https://doi.org/10.1007/BF03167269