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Uspekhi Mat. Nauk, 1967, Volume 22, Issue 2(134), Pages 59–107 (Mi umn5728)  

This article is cited in 47 scientific papers (total in 47 papers)

On the approximate solution of problems in mathematical physics

V. D. Kupradze

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English version:
Russian Mathematical Surveys, 1967, 22:2, 58–108

Bibliographic databases:

UDC: 517.946
MSC: 78A25, 78A45, 35A35, 35J25

Citation: V. D. Kupradze, “On the approximate solution of problems in mathematical physics”, Uspekhi Mat. Nauk, 22:2(134) (1967), 59–107; Russian Math. Surveys, 22:2 (1967), 58–108

Citation in format AMSBIB
\by V.~D.~Kupradze
\paper On the approximate solution of problems in mathematical physics
\jour Uspekhi Mat. Nauk
\yr 1967
\vol 22
\issue 2(134)
\pages 59--107
\jour Russian Math. Surveys
\yr 1967
\vol 22
\issue 2
\pages 58--108

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    3. Ralph E Kleinman, Wolfgang L Wendland, “On Neumann's method for the exterior Neumann problem for the Helmholtz equation”, Journal of Mathematical Analysis and Applications, 57:1 (1977), 170  crossref
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