Abstract
This paper describes an integral equation method for computing the conformal mapping of a finite doubly-connected domain ontoR <|w|<1, whereR is uniquely determined. The method is illustrated by numerical examples.
Similar content being viewed by others
References
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 mapping 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 mapping 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 mapping. Num. Math.9, 250–258 (1966).
—— Numerical mapping of exterior domains. Num. Math.10, 437–445 (1967)
Ugodčikov, A. G.: Electromodelling of the conformal mapping of a circular cylinder onto a given doubly connected region. Ukrain. Mat. Ž.7, 305–312 (1955)
Wilson, H. B.: A method of conformal mapping and the determination of stresses in solid propellant rocket grains. Report No. S-38, Rohm and Haas Co., Alabama, 1963
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Symm, G.T. Conformal mapping of doubly-connected domains. Numer. Math. 13, 448–457 (1969). https://doi.org/10.1007/BF02163272
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02163272