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A numerical comparison of integral equations of the first and second kind for conformal mapping

Authors: John K. Hayes, David K. Kahaner and Richard G. Kellner
Journal: Math. Comp. 29 (1975), 512-521
MSC: Primary 65E05; Secondary 30A28
MathSciNet review: 0371036
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Abstract: Two methods for computing numerical conformal mappings are compared. The first, due to Symm, uses a Fredholm integral equation of the first kind while the other, due to Lichtenstein, uses a Fredholm integral equation of the second kind. The two methods are tested on ellipses with different ratios of major to minor axes. The method based on the integral equation of the second kind is superior if the ratio is less than or equal to 2.5. The opposite is true if the ratio is greater than or equal to 10. Similar results are obtained for other regions.

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Keywords: Numerical conformal mapping, numerical solution of integral equations of the first kind
Article copyright: © Copyright 1975 American Mathematical Society