Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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] B. Noble, Methods based on the Wiener-Hopf technique for the solution of partial differential equations, International Series of Monographs on Pure and Applied Mathematics. Vol. 7, Pergamon Press, New York-London-Paris-Los Angeles, 1958. MR 0102719
  • [2] N. I. Muskhelishvili, Singular integral equations, Wolters-Noordhoff Publishing, Groningen, 1972. Boundary problems of functions theory and their applications to mathematical physics; Revised translation from the Russian, edited by J. R. M. Radok; Reprinted. 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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