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Uspekhi Mat. Nauk, 1976, Volume 31, Issue 6(192), Pages 167–197 (Mi umn4014)  

This article is cited in 5 scientific papers (total in 6 papers)

Difference approximation methods for problems of mathematical physics

A. A. Samarskii, I. V. Fryazinov


Abstract: In the paper we construct and investigate conservative schemes for elliptic equations in an arbitrary domain. To obtain difference approximations in the case of equations with mixed derivatives and with boundary conditions of the third kind, the concept of a vector scheme proves to be useful. Vector difference schemes are constructed by means of the integro-interpolation method (balance method).
To obtain economical algorithms for the solution of many-dimensional parabolic problems we use the method of summary approximations, which leads to additive schemes and vector additive schemes. In particular, we construct economical additive vector schemes for parabolic equations with boundary conditions of the third kind in an arbitrary domain.

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English version:
Russian Mathematical Surveys, 1976, 31:6, 179–213

Bibliographic databases:

UDC: 517.9
MSC: 35R10, 35J05, 35J25
Received: 20.07.1976

Citation: A. A. Samarskii, I. V. Fryazinov, “Difference approximation methods for problems of mathematical physics”, Uspekhi Mat. Nauk, 31:6(192) (1976), 167–197; Russian Math. Surveys, 31:6 (1976), 179–213

Citation in format AMSBIB
\Bibitem{SamFry76}
\by A.~A.~Samarskii, I.~V.~Fryazinov
\paper Difference approximation methods for~problems of~mathematical physics
\jour Uspekhi Mat. Nauk
\yr 1976
\vol 31
\issue 6(192)
\pages 167--197
\mathnet{http://mi.mathnet.ru/umn4014}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=455447}
\zmath{https://zbmath.org/?q=an:0357.65073|0367.65049}
\transl
\jour Russian Math. Surveys
\yr 1976
\vol 31
\issue 6
\pages 179--213
\crossref{https://doi.org/10.1070/RM1976v031n06ABEH001587}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. N. Tikhonov, A. V. Bitsadze, V. A. Il'in, A. G. Sveshnikov, A. A. Arsen'ev, “Aleksandr Andreevich Samarskii (on his sixtieth birthday)”, Russian Math. Surveys, 35:1 (1980), 241–253  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. N. Muchynski, V. A. Tsurko, “Additive difference schemes for solving parabolic equations with mixed derivatives”, Comput. Math. Math. Phys., 33:3 (1993), 357–364  mathnet  mathscinet  zmath  isi
    3. P. N. Vabishchevich, “Vector additive difference schemes for first-order evolution equations”, Comput. Math. Math. Phys., 36:3 (1996), 317–322  mathnet  mathscinet  zmath  isi
    4. P. N. Vabishchevich, A. A. Samarskii, “Finite difference schemes for convection-diffusion problems on irregular meshes”, Comput. Math. Math. Phys., 40:5 (2000), 692–704  mathnet  mathscinet  zmath  elib
    5. D. Pissarenko, G. Reshetova, V. Tcheverda, “3D finite-difference synthetic acoustic log in cylindrical coordinates”, Journal of Computational and Applied Mathematics, 234:6 (2010), 1766  crossref
    6. R Usmanov, K Seitnazarov, “The Information Model for Hydrogeological Object and its Fuzzy-Deterministic Model”, Adv. Sci, 2014:7 (2014), 67  crossref
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