An improved method for numerical conformal mapping

Authors:
John K. Hayes, David K. Kahaner and Richard G. Kellner

Journal:
Math. Comp. **26** (1972), 327-334

MSC:
Primary 30A28

DOI:
https://doi.org/10.1090/S0025-5718-1972-0301176-8

MathSciNet review:
0301176

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Abstract | References | Similar Articles | Additional Information

Abstract: A new technique for the numerical conformal mapping of a planar region onto the unit disk has been presented and tested by Symm. By elaborating on his methods, we have improved the accuracy of the numerical results by up to four orders of magnitude. For illustration, our methods have been applied to several of the same regions considered in the literature by Symm and Rabinowitz. A flexible FORTRAN code and User's Guide are reproduced on the microfiche card in this issue.

**[1]**J. Hayes,*Four Computer Programs Using Green's Third Formula to Numerically Solve Laplace's Equation in Inhomogeneous Media*, Los Alamos Scientific Laboratory Report, LA-4423, April 1970.**[2]**J. Hayes & R. Kellner,*The Eigenvalue Problem for a Pair of Coupled Integral Equations Arising in the Numerical Solution of Laplace's Equation*, Los Alamos Scientific Laboratory Report, LA-DC-12009, October 1970.**[3]**M. A. Jaswon, ``Integral equation methods in potential theory. I,''*Proc. Roy. Soc. Ser. A*, v. 275, 1963, pp. 23-32. MR**27**#4034. MR**0154075 (27:4034)****[4]**M. Maiti, ``A note on the integral equation methods in potential theory,''*Quart. Appl. Math.*, v. 25, 1968, pp. 480-484. MR**37**#447. MR**0224848 (37:447)****[5]**N. I. Muskhelišvili,*Singular Integral Equations. Boundary Problems of Function Theory and their Application to Mathematical Physics*, OGIZ, Moscow, 1946; English transl., Noordhoff, Groningen, 1953. MR**8**, 586; MR**15**, 434. MR**0355494 (50:7968)****[6]**Philip Rabinowitz, ``Numerical experiments in conformal mapping by the method of orthonormal polynomials,''*J. Assoc. Comput. Mach.*, v. 13, 1966, pp. 296-303.**[7]**G. T. Symm, ``An integral equation method in conformal mapping,''*Numer. Math.*, v. 9, 1966, pp. 250-258. MR**34**#7056. MR**0207240 (34:7056)****[8]**G. T. Symm, ``Numerical mapping of exterior domains,''*Numer. Math.*, v. 10, 1967, pp. 437-445. MR**36**#3525. MR**0220465 (36:3525)****[9]**G. T. Symm, ``Conformal mapping of doubly-connected domains,''*Numer. Math.*, v. 13, 1969, pp. 448-457. MR**40**#3736. MR**0250502 (40:3736)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1972-0301176-8

Keywords:
Numerical conformal mapping,
numerical solution of integral equations of the first kind

Article copyright:
© Copyright 1972
American Mathematical Society