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Mat. Zametki, 1969, Volume 6, Issue 1, Pages 91–96 (Mi mz6901)  

This article is cited in 2 scientific papers (total in 2 papers)

Ritz method for equations with small parameters for higher derivatives

L. A. Kalyakin

V. A. Steklov Institute of Mathematics, Sverdlovsk Branch of the Academy of Sciences of USSR

Abstract: The problem of convergence of the Ritz method is considered for positive definite operational equations of the form $a_\varepsilon u\equiv(\varepsilon A_1+A_0)u=f$ containing small parameters $\varepsilon$ for the principal part. For specific natural conditions it is proved that the Ritz method, used for an approximate solution to such equations, converges to an exact solution in a metric with quadratic form uniformly with respect to the parameter $\varepsilon$.

Full text: PDF file (394 kB)

English version:
Mathematical Notes, 1969, 6:1, 513–516

Bibliographic databases:

UDC: 518
Received: 09.07.1968

Citation: L. A. Kalyakin, “Ritz method for equations with small parameters for higher derivatives”, Mat. Zametki, 6:1 (1969), 91–96; Math. Notes, 6:1 (1969), 513–516

Citation in format AMSBIB
\Bibitem{Kal69}
\by L.~A.~Kalyakin
\paper Ritz method for equations with small parameters for higher derivatives
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 1
\pages 91--96
\mathnet{http://mi.mathnet.ru/mz6901}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=257768}
\zmath{https://zbmath.org/?q=an:0207.16502|0197.43302}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 1
\pages 513--516
\crossref{https://doi.org/10.1007/BF01450256}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. A. Kalyakin, “Galerkin's method for equations with a small parameter in the highest order derivatives”, Math. USSR-Sb., 14:4 (1971), 525–536  mathnet  crossref  mathscinet  zmath
    2. 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
  • Математические заметки Mathematical Notes
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