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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 2, Pages 264–281 (Mi zvmmf182)  

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

Application of wavelet transforms to the solution of boundary value problems for linear parabolic equations

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

Neftegasproekt, pr. Zardabi 88, Baku, 370112, Azerbaijan

Abstract: A method based on wavelet transforms is proposed for finding weak solutions to initial-boundary value problems for linear parabolic equations with discontinuous coefficients and inexact data. In the framework of multiresolution analysis, the general scheme for finite-dimensional approximation in the regularization method is combined with the discrepancy principle. An error estimate is obtained for the stable approximate solution obtained by solving a set of linear algebraic equations for the wavelet coefficients of the desired solution.

Key words: weak solutions to initial-boundary value problems, linear parabolic equations, distributional derivative, wavelet transform, multiresolution analysis, finite-dimensional approximation scheme.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:2, 251–268

Bibliographic databases:

UDC: 519.633
Received: 29.11.2005
Revised: 06.08.2007

Citation: E. M. Abbasov, O. A. Dyshin, B. A. Suleimanov, “Application of wavelet transforms to the solution of boundary value problems for linear parabolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 48:2 (2008), 264–281; Comput. Math. Math. Phys., 48:2 (2008), 251–268

Citation in format AMSBIB
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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. E. M. Abbasov, O. A. Dyshin, B. A. Suleimanov, “Wavelet method for solving the unsteady porous-medium flow problem with discontinuous coefficients”, Comput. Math. Math. Phys., 48:12 (2008), 2194–2210  mathnet  crossref  mathscinet  isi  elib
    2. E. M. Abbasov, O. A. Dyshin, B. A. Suleimanov, “Wavelet method for solving second-order quasilinear parabolic equations with a conservative principal part”, Comput. Math. Math. Phys., 49:9 (2009), 1554–1566  mathnet  crossref  zmath  isi  elib
    3. Amirov F.G., “Analiz perekhodnykh protsessov v rabote vetroenergeticheskoi ustanovki s primeneniem veivlet-preobrazovaniya”, Vestnik mashinostroeniya, 2010, no. 1, 90–92  mathscinet  elib
    4. Dyshin O.A., “Differentsirovanie diskretnykh veivlet-razlozhenii funktsii mnogikh peremennykh”, Nauchnye trudy NIPI Neftegaz GNKAR, 2010, no. 4, 73–79  elib
    5. 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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