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Mat. Zametki, 1974, Volume 15, Issue 4, Pages 595–602 (Mi mz7383)  

Methods of solving Fredholm equations optimal on classes of functions

A. F. Shapkin

Gor'kii State University

Abstract: This paper is devoted to the solution of linear Fredholm equations in the unit $s$-dimensional cube for classes of functions with a dominant mixed derivative of order $r$ in each variable. We present an algorithm for obtaining the solution over the whole domain with an error $O(N^{-r}\ln^{2s-1}N)$ in the uniform metric using the values of the given functions at $O(N\ln^{2s-1}N)$ points and consisting of $O(N\ln^{2s-1}N)$ elementary operations. We show that these estimates can only be improved at the expense of the exponent of $\ln N$.

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English version:
Mathematical Notes, 1974, 15:4, 351–355

Bibliographic databases:

UDC: 513.88
Received: 19.05.1972

Citation: A. F. Shapkin, “Methods of solving Fredholm equations optimal on classes of functions”, Mat. Zametki, 15:4 (1974), 595–602; Math. Notes, 15:4 (1974), 351–355

Citation in format AMSBIB
\Bibitem{Sha74}
\by A.~F.~Shapkin
\paper Methods of solving Fredholm equations optimal on classes of functions
\jour Mat. Zametki
\yr 1974
\vol 15
\issue 4
\pages 595--602
\mathnet{http://mi.mathnet.ru/mz7383}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=403273}
\zmath{https://zbmath.org/?q=an:0308.45016}
\transl
\jour Math. Notes
\yr 1974
\vol 15
\issue 4
\pages 351--355
\crossref{https://doi.org/10.1007/BF01095127}


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