Abstract
This paper describes an integral equation method for computing the conformal map** of a finite doubly-connected domain ontoR <|w|<1, whereR is uniquely determined. The method is illustrated by numerical examples.
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Gaier, D.: Konstruktive Methoden der konformen Abbildung. Springer Tracts in Natural Philosophy, Vol. 3. Berlin-Göttingen-Heidelberg-New York: Springer 1964.
Garrick, I. E.: Potential flow about arbitrary biplane wing sections. NACA Report 542, 1936.
Jaswon, M. A.: Integral equation methods in potential theory. I. Proc. Roy. Soc. A275, 23–32 (1963).
Kantorovich, L. V., Krylov, V. I.: Approximate methods of higher analysis. Groningen: Noordhoff 1964.
Laura, P. A.: Conformal map** of a class of doubly connected regions. NASA Tech. Rep. No. 8, The Catholic University of America, Washington, 1965
Lewis, G. K.: Flow and load parameters of hydrostatic oil bearings for several port shapes. J. Mech. Eng. Sci.8, 173–184 (1966).
Mikhlin, S. G.: Integral equations. London: Pergamon 1957.
Muskhelishvili, N. I.: Some basic problems of the mathematical theory of elasticity. Groningen: Noordhoff 1953.
Opfer, G.: Untere, beliebig verbesserbare Schranken für den Modul eines zweifach zusammenhängenden Gebietes mit Hilfe von Differenzenverfahren. Dissertation, Hamburg, 1967.
Royden, H. L.: A modification of the Neumann-Poincaré method for multiply connected regions. Pacific J. Maths.2, 385–394 (1952).
Savin, G. N.: Stress concentration around holes. London: Pergamon 1961.
Sugiyama, H., Joh, K.: A numerical procedure of conformal map** in case of simply, doubly and multiply connected domains from the viewpoint of Monte Carlo approach (I). Tech. Rep. Osaka Univ.12, No. 488 (1962).
Symm, G. T.: An integral equation method in conformal map**. Num. Math.9, 250–258 (1966).
—— Numerical map** of exterior domains. Num. Math.10, 437–445 (1967)
Ugodčikov, A. G.: Electromodelling of the conformal map** of a circular cylinder onto a given doubly connected region. Ukrain. Mat. Ž.7, 305–312 (1955)
Wilson, H. B.: A method of conformal map** and the determination of stresses in solid propellant rocket grains. Report No. S-38, Rohm and Haas Co., Alabama, 1963
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Symm, G.T. Conformal map** of doubly-connected domains. Numer. Math. 13, 448–457 (1969). https://doi.org/10.1007/BF02163272
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DOI: https://doi.org/10.1007/BF02163272