Mathematics of Computation

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

 

 

Existence of a solution to the discrete Theodorsen equation for conformal mappings


Author: Martin H. Gutknecht
Journal: Math. Comp. 31 (1977), 478-480
MSC: Primary 30A28; Secondary 65E05
MathSciNet review: 0440021
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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 [Enhancements On Off] (What's this?)

  • [1] Lothar Collatz, Functional analysis and numerical mathematics, Translated from the German by Hansjörg Oser, Academic Press, New York-London, 1966. MR 0205126
  • [2] Dieter Gaier, Konstruktive Methoden der konformen Abbildung, Springer Tracts in Natural Philosophy, Vol. 3, Springer-Verlag, Berlin, 1964 (German). MR 0199360
  • [3] 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, 10.1007/BF01395955

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1977-0440021-1
Keywords: Discrete Theodorsen equation, Theodorsen's integral equation, numerical conformal mapping, Brouwer's fixed point theorem
Article copyright: © Copyright 1977 American Mathematical Society