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The use of splines and singular functions in an integral equation method for conformal mapping. (English) Zbl 0441.30016


MSC:

30C30 Schwarz-Christoffel-type mappings
41A15 Spline approximation
65D07 Numerical computation using splines
65R20 Numerical methods for integral equations
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References:

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[4] Gaier, D.: Integralgleichungen erster Art und konforme Abbildung. Math. Z.147, 113-129 (1976) · Zbl 0312.30006 · doi:10.1007/BF01164277
[5] Hayes, J.K., Kahaner, D.K., Kellner, R.G.: An improved method for numerical conformal mapping. Math. Comput.26, 327-334 (1972) · Zbl 0239.65033 · doi:10.1090/S0025-5718-1972-0301176-8
[6] Hayes, J.K., Kahaner, D.K., Kellner, R.G.: A comparison of integral equations of the first and second kind for conformal mapping. Math. Comput.29, 512-521 (1975) · Zbl 0305.30012 · doi:10.1090/S0025-5718-1975-0371036-8
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[9] Jaswon, M.A., Symm, G.T.: Integral equation methods in potential theory and elastostatics. London: Academic Press 1977 · Zbl 0414.45001
[10] Levin, D., Papamichael, N., Sideridis, A.: The Bergman kernel method for the numerical conformal mapping of simply connected domains. J. Inst. Math. Appl.22, 171-187 (1978) · Zbl 0391.30008 · doi:10.1093/imamat/22.2.171
[11] Milne-Thomson, L.M.: Jacobian elliptic function tables. New York: Dover Publications 1950 · Zbl 0041.44702
[12] Papamichael, N., Sideridis, A.: Formulae for the approximate conformal mapping of some simply connected domains. Technical Report TR/72, Dept of Maths, Brunel University 1977 · Zbl 0372.31001
[13] Symm, G.T.: An integral equation method in conformal mapping. Numer. Math.9, 250-258 (1966) · Zbl 0156.16901 · doi:10.1007/BF02162088
[14] Symm, G.T.: Problems in two-dimensional potential theory. Numerical Solution of integral equations. (L.M. Delves, J. Walsh eds.). Oxford: Clarendon Press 1974
[15] Symm, G.T.: The Robin problem for Laplace’s equation. New developments in boundary element methods (C.A. Brebbia ed.) Southampton: CML Publications 1980 · Zbl 0443.65094
[16] Wendland, W.L.: On Galerkin collocation methods for integral equations of elliptic boundary value problems. Intern. Ser. Numerical Mathematics. Basel: Birkhäuser (1981, in press)
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