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On conformal mapping of polygonal regions

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Abstract

We develop Kufarev's method for determining unknown parameters in the Schwarz-Christoffel integral in the case of conformal mapping of polygonal regions with boundary normalization.

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References

  1. R. Schinzinger and P. Laura,Conformal Mapping: Methods and Applications, Elsevier, Amsterdam (1991).

    Google Scholar 

  2. M. A. Lavrent'yev and B. V. Shabat,Methods of the Theory of a Complex Variable [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  3. D. Gaier,Konstruktive Methoden der Konformen Abbildung, Springer, Berlin (1964).

    Google Scholar 

  4. L. Trefethen, “Numerical computation of the Schwarz-Christoffel transformation,”S1AM J. Sci. Stat. Comput.,1, No. 1, 82–102 (1980).

    Google Scholar 

  5. P. P. Kufarev, “On a method for numerical calculation of parameters in the Schwarz-Christoffel integral,”Dokl. Akad. Nauk Ukr. SSR,57, No. 6, 535–537 (1947).

    Google Scholar 

  6. I. A. Aleksandrov,Parametric Extensions in the Theory of Univalent Functions [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  7. Ch. Lowner, “Untersuchungen uber schlichte konforme Abbildungen des Einheitskreises,”Math. Ann.,89, 103–121 (1923).

    Google Scholar 

  8. T. R. Hopkins and D. E. Roberts, “Kufarev's method for determining the Schwarz-Christoffel parameters,”Numer. Math.,33, 353–365 (1979).

    Google Scholar 

  9. Ch. Lowner,Collected Papers, Birkhauser, Boston-Basel (1988).

    Google Scholar 

  10. V. V. Goryainov, “Semigroups of conformal mappings,”Mat. Sb,129, No. 4, 451–472 (1986).

    Google Scholar 

  11. B. V. Shabat,Introduction to Complex Analysis [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  12. G. M. Galuzin,Geometric Theory of Functions of a Complex Variable, American Mathematical Society, Translations of Mathematical Monographs, 26, Providence, R. I. (1969).

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 11, pp. 1484–1494, November, 1993.

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Gutlyanskii, V.Y., Zaidan, A.O. On conformal mapping of polygonal regions. Ukr Math J 45, 1669–1680 (1993). https://doi.org/10.1007/BF01060857

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  • DOI: https://doi.org/10.1007/BF01060857

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