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References
S. Bergman, The kernel function and conformal mapping. Math. Surveys 5 (A.M.S., Providence, R.I., 2nd ed., 1970).
F. Bowman, Introduction to Elliptic Functions (English University Press, London, 1950).
T. Carleman, Über die Approximation analytischer Functionen durch lineare Aggregate von vorgegebenen Potenzen, Ark. Mat. Astr. Fys. 17 (1923) 1–30.
E.T. Copson, Partial Differential Equations (Cambridge University Press, London, 1975).
W. Eidel, Konforme Abbildung mehrfach zusammenhängender Gebiete durch Lösung von Variationsproblemen, Diplomarbeit Giessen, 1979.
D. Gaier, Konstruktive Methoden der Konformen Abbildung (Springer Verlag, Berlin, 1964).
D. Gaier, Vorlesengen über Approximation im Komplexen (Bïrkhauser Verlag, Basel, 1980).
P. Henrici, Applied and Computational Complex Analysis, Vol. 1 (Wiley, New York, 1974).
L.V. Kantorovich and V.I. Krylov, Approximate Methods of Higher Analysis (Wiley, New York, 1964).
P.A.A. Laura, A survey of modern applications of the method of conformal mapping, Revista De La Union Mathematica Argentina 27 (1975) 167–179.
R.S. Lehman, Development of the mapping function at an analytic corner, Pacific J. Math. 7 (1957) 1437–1449.
D. Levin, N. Papamichael and A? Sideridis, The Bergman kernel method for the numerical conformal mapping of simply-connected domains, J. Inst. Math. Appl. 22 (1978) 171–187.
G.K. Lewis, Flow and load parameters of hydrostatic oil bearing for several port shapes, J. Mech. Engrg. Sci. 8 (1966) 173–184.
Z. Nehari, Conformal mapping (McGraw-Hill, New York, 1952).
N. Papamichael and C.A. Kokkinos, Two numerical methods for the conformal mapping of simply-connected domains, Comput. Meths. Appl. Mech. Engrg. 28 (1981) 285–307.
N. Papamichael and C.A. Kokkinos, Numerical conformal mapping of exterior domains, Comput. Meths. Appl. Mech. Engrg. 31 (1982) 189–203.
N. Papamichael and C.A. Kokkinos, The use of singular functions for the approximate conformal mapping of doubly-connected domains, Tech. Rep. TR/01/82, Dept. of Maths., Brunel University 1982. (To appear in SIAM J. Sci. Stat. Comput.).
N. Papamichael, M.K. Warby and D.M. Hough, The determination of the poles of the mapping function and their use in numerical conformal mapping, J. Comp. Appl. Maths. 9 (1983) 155–166.
N. Papamichael and M.K. Warby, Pole-type-singularities and the numerical conformal mapping of doubly-connected domains, J. Comp. Appl. Maths. (1984, in press).
N. Papamichael and M.K. Warby, Stability and convergence properties of kernel function methods for numerical conformal mapping, Tech. Rept., Dept. of Maths. and Stats., Brunel University. In preparation.
G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics (Princeton University Press, Princeton, N.J., 1951).
G. Sansone and J. Gerretsen, Lectures on the Theory of Functions of a Complex Variable, Vol. II (Walters-Noordhoff, Groningen, 1969).
I.B. Simonenko, On the convergence of Bieberbach polynomials in the case of a Lipschitz domain, Math. USSR Izvestija, 13 (1979) 166–174.
J.F. Thompson, Z.U.A. Warsi and C.W. Masti, Boundary fitted coordinate systems for numerical solution of partial differential equations. J. Comp. Phys. 47 (1982) 1–108.
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Papamichael, N. (1985). The treatment of singularities in orthonormalization methods for numerical conformal mapping. In: Grisvard, P., Wendland, W.L., Whiteman, J.R. (eds) Singularities and Constructive Methods for Their Treatment. Lecture Notes in Mathematics, vol 1121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076273
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DOI: https://doi.org/10.1007/BFb0076273
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