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Mat. Sb. (N.S.), 1971, Volume 85(127), Number 4(8), Pages 527–537 (Mi msb3276)  

This article is cited in 1 scientific paper (total in 1 paper)

Galerkin's method for equations with a small parameter in the highest order derivatives

L. A. Kalyakin


Abstract: The question considered is the convergence of Galerkin's method for the operator equation $A_\varepsilon u-Ku\equiv\varepsilon A_1u+A_0u-Ku=f$, where $A_0$ is positive definite, $A_1$ is positive semidefinite with domain of definition $D(A_1)\subset D(A_0)$, and $\varepsilon>0$ is a small parameter. With certain additional natural assumptions it is shown that the solution obtained by Galerkin's method is uniformly convergent to the true solution in the norm defined by the quadratic form $(A_\varepsilon u,u)$ for $0\leqslant\varepsilon\leqslant1$.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Sbornik, 1971, 14:4, 525–536

Bibliographic databases:

UDC: 517.946.9
MSC: 65N30
Received: 06.05.1970

Citation: L. A. Kalyakin, “Galerkin's method for equations with a small parameter in the highest order derivatives”, Mat. Sb. (N.S.), 85(127):4(8) (1971), 527–537; Math. USSR-Sb., 14:4 (1971), 525–536

Citation in format AMSBIB
\Bibitem{Kal71}
\by L.~A.~Kalyakin
\paper Galerkin's method for equations with a~small parameter in the highest order derivatives
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 85(127)
\issue 4(8)
\pages 527--537
\mathnet{http://mi.mathnet.ru/msb3276}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=283589}
\zmath{https://zbmath.org/?q=an:0242.35068}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 14
\issue 4
\pages 525--536
\crossref{https://doi.org/10.1070/SM1971v014n04ABEH002818}


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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. L. A. Kalyakin, “On approximate methods of solving nonlinear boundary value problems with a small parameter”, Math. USSR-Sb., 28:4 (1976), 491–500  mathnet  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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