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Zh. Vychisl. Mat. Mat. Fiz., 1990, Volume 30, Number 7, Pages 1031–1044 (Mi zvmmf3232)  

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

The projection method for singularly perturbed boundary value problems

I. A. Blatov

Voronezh

Abstract: A finite element method for linear and non-linear singularly perturbed boundary-value problems is considered. It is proved that the approximate solutions converge to the exact solution in the norm of the space of continuous functions, uniformly in the small parameter. The proposed scheme is suitable for solving a wider class of problems than can be handled by the popular Уhinged element methodФ, and also produces a higher order of approximation.

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English version:
USSR Computational Mathematics and Mathematical Physics, 1990, 30:4, 47–56

Bibliographic databases:

UDC: 519.62
MSC: Primary 65L10; Secondary 65L60, 34B15, 34E15
Received: 05.05.1988
Revised: 25.09.1989

Citation: I. A. Blatov, “The projection method for singularly perturbed boundary value problems”, Zh. Vychisl. Mat. Mat. Fiz., 30:7 (1990), 1031–1044; U.S.S.R. Comput. Math. Math. Phys., 30:4 (1990), 47–56

Citation in format AMSBIB
\Bibitem{Bla90}
\by I.~A.~Blatov
\paper The projection method for singularly perturbed boundary value problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1990
\vol 30
\issue 7
\pages 1031--1044
\mathnet{http://mi.mathnet.ru/zvmmf3232}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1070548}
\zmath{https://zbmath.org/?q=an:0714.65073}
\transl
\jour U.S.S.R. Comput. Math. Math. Phys.
\yr 1990
\vol 30
\issue 4
\pages 47--56
\crossref{https://doi.org/10.1016/0041-5553(90)90043-R}


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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. Andreev V.B., Kopteva N.V., “On the convergence, uniform with respect to a small parameter, of monotone three-point finite-difference approximations”, Differ Equ, 34:7 (1998), 921–929  mathscinet  zmath  isi
    2. V. B. Andreev, “Convergence of a modified Samarskij's monotonic scheme on a smoothly condensing grid”, Comput. Math. Math. Phys., 38:8 (1998), 1212–1224  mathnet  mathscinet  zmath
    3. Kadalbajoo M.K., Gupta V., “A brief survey on numerical methods for solving singularly perturbed problems”, Applied Mathematics and Computation, 217:8 (2010), 3641–3716  crossref  mathscinet  zmath  isi
    4. I. A. Blatov, E. V. Kitaeva, “Convergence of the adapting grid method of Bakhvalov's type for singularly perturbed boundary value problems”, Num. Anal. Appl., 9:1 (2016), 34–44  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. I. A. Blatov, N. V. Dobrobog, E. V. Kitaeva, “Conditional $\varepsilon$-uniform boundedness of Galerkin projectors and convergence of an adaptive mesh method as applied to singularly perturbed boundary value problems”, Comput. Math. Math. Phys., 56:7 (2016), 1293–1304  mathnet  crossref  crossref  isi  elib
  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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