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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 9, Pages 1629–1642 (Mi zvmmf4755)  

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

Wavelet method for solving second-order quasilinear parabolic equations with a conservative principal part

E. m. Abbasov, O. A. Dyshin, B. A. Suleimanov

Institute Neftegasproekt GNKAR, pr. Zardabi 88, Baku, Az 1012, Azerbaijan

Abstract: A method based on wavelet transforms is proposed for finding classical solutions to initial-boundary value problems for second-order quasilinear parabolic equations. For smooth data, the convergence of the method is proved and the convergence rate of an approximate weak solution to a classical one is estimated in the space of wavelet coefficients. An approximate weak solution of the problem is found by solving a nonlinear system of equations with the help of gradient-type iterative methods with projection onto a fixed subspace of basis wavelet functions.

Key words: weak and approximate weak solutions to initial-boundary value problems for parabolic equations, multiresolution analysis, wavelet basis, gradient-type iterative method, irregular operator equation.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:9, 1554–1566

Bibliographic databases:

UDC: 519.63
Received: 11.08.2008

Citation: E. M. Abbasov, O. A. Dyshin, B. A. Suleimanov, “Wavelet method for solving second-order quasilinear parabolic equations with a conservative principal part”, Zh. Vychisl. Mat. Mat. Fiz., 49:9 (2009), 1629–1642; Comput. Math. Math. Phys., 49:9 (2009), 1554–1566

Citation in format AMSBIB
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\paper Wavelet method for solving second-order quasilinear parabolic equations with a~conservative principal part
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
\vol 49
\issue 9
\pages 1629--1642
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\zmath{https://zbmath.org/?q=an:05649703}
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\transl
\jour Comput. Math. Math. Phys.
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\pages 1554--1566
\crossref{https://doi.org/10.1134/S0965542509090103}
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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. Dyshin O.A., “Differentsirovanie diskretnykh veivlet-razlozhenii funktsii mnogikh peremennykh”, Nauchnye trudy NIPI Neftegaz GNKAR, 2010, no. 4, 73–79  elib
    2. Suleimanov B.A., Dyshin O.A., “Application of Discrete Wavelet Transform to the Solution of Boundary Value Problems for Quasi-Linear Parabolic Equations”, Appl. Math. Comput., 219:12 (2013), 7036–7047  crossref  mathscinet  zmath  isi  elib  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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