Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Iterative solutions of Wiener-Hopf integral equations

Authors: Tai Te Wu and Tai Tsun Wu
Journal: Quart. Appl. Math. 20 (1963), 341-352
MSC: Primary 45.15
DOI: https://doi.org/10.1090/qam/141962
MathSciNet review: 141962
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Abstract: A method of iteration is used to study integral equations of the Wiener-Hopf type. In the case of a single integral equation, it is found that the iterative solution can be summed to give the known results. In the case of two coupled integral equations, where the general solution is not known, the iterative solution can be reduced to expressions in closed form, in the sense of a finite number of quadratures, only in some very special cases. Two such special cases are discussed in detail.

References [Enhancements On Off] (What's this?)

  • [1] See, for example, B. Noble, The Wiener-Hopf technique, Pergamon Press (1958) MR 0102719
  • [2] N. I. Muskhelishvili, Singular integral equations, Noordhoff Press (1953) MR 0355494
  • [3] E. C. Titchmarsh, Theory of Fourier integrals, Clarendon Press (1948)
  • [4] See p. 56 of reference 2
  • [5] See p. 37 of reference 2

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DOI: https://doi.org/10.1090/qam/141962
Article copyright: © Copyright 1963 American Mathematical Society

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