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Sib. Zh. Ind. Mat., 2005, Volume 8, Number 1, Pages 117–128 (Mi sjim324)  

This article is cited in 4 scientific papers (total in 4 papers)

Approximate solution of a mixed problem for a parabolic equation by means of a special basis of functions

V. V. Smelov

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences

Abstract: Using the eigenfunctions of two Sturm–Liouville problems (with the same operator of the most general form but two different sets of boundary conditions), we propose a method for construction of specific basis functions such that the corresponding expansions of smooth and piecewise smooth functions lead to fast converging series. The last circumstance can be successfully employed for approximate solution of mixed problems for a parabolic equation when the sought function is approximated in the spatial variables by few basis functions. First, the case of one spatial coordinate is elaborated and the two-dimensional case is briefly discussed in Section 5. The method aims primarily at the case when the sought function is piecewise smooth in the spatial variable and the implementation of the method bases on the concept of generalized solution.

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English version:
Journal of Applied and Industrial Mathematics, 2007, 1:1, 105–115

Bibliographic databases:

UDC: 518.12:519.34
Received: 06.12.2004

Citation: V. V. Smelov, “Approximate solution of a mixed problem for a parabolic equation by means of a special basis of functions”, Sib. Zh. Ind. Mat., 8:1 (2005), 117–128; J. Appl. Industr. Math., 1:1 (2007), 105–115

Citation in format AMSBIB
\Bibitem{Sme05}
\by V.~V.~Smelov
\paper Approximate solution of a~mixed problem for a~parabolic equation by means of a~special basis of functions
\jour Sib. Zh. Ind. Mat.
\yr 2005
\vol 8
\issue 1
\pages 117--128
\mathnet{http://mi.mathnet.ru/sjim324}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2221675}
\transl
\jour J. Appl. Industr. Math.
\yr 2007
\vol 1
\issue 1
\pages 105--115
\crossref{https://doi.org/10.1134/S1990478907010115}


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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. Smelov, VV, “Gauss type quadratures based on trigonometric bases”, Russian Journal of Numerical Analysis and Mathematical Modelling, 23:3 (2008), 265  crossref  mathscinet  zmath  isi  scopus
    2. V. V. Smelov, A. S. Popov, “An analog to Gaussian quadrature implemented on a specific trigonometric basis”, Num. Anal. Appl., 3:4 (2010), 357–366  mathnet  crossref
    3. Smelov V.V., “Construction of a Functional Basis with Automatic Fulfillment of Interface Conditions at Discontinuity Points of Coefficients of an Elliptic Operator”, Russ. J. Numer. Anal. Math. Model, 27:4 (2012), 387–398  crossref  mathscinet  zmath  isi  elib  scopus
    4. V. V. Smelov, “Osnovannye na trigonometrii bazisy i ikh preimuschestva”, Vestn. NGU. Ser. matem., mekh., inform., 13:1 (2013), 105–119  mathnet
  • Сибирский журнал индустриальной математики
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