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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Existence of a solution to the discrete Theodorsen equation for conformal mappings
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by Martin H. Gutknecht PDF
Math. Comp. 31 (1977), 478-480 Request permission

Abstract:

The discrete Theodorsen equation is the basis of efficient numerical methods for conformal mappings of the unit disk onto Jordan regions that are starlike with respect to the origin. Applying Brouwer’s fixed point theorem we show here that there always exists a solution to this equation.
References
  • Lothar Collatz, Functional analysis and numerical mathematics, Academic Press, New York-London, 1966. Translated from the German by Hansjörg Oser. MR 0205126
  • Dieter Gaier, Konstruktive Methoden der konformen Abbildung, Springer Tracts in Natural Philosophy, Vol. 3, Springer-Verlag, Berlin, 1964 (German). MR 0199360
  • Martin H. Gutknecht, Solving Theodorsen’s integral equation for conformal maps with the fast Fourier transform and various nonlinear iterative methods, Numer. Math. 36 (1980/81), no. 4, 405–429. MR 614857, DOI 10.1007/BF01395955
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Math. Comp. 31 (1977), 478-480
  • MSC: Primary 30A28; Secondary 65E05
  • DOI: https://doi.org/10.1090/S0025-5718-1977-0440021-1
  • MathSciNet review: 0440021