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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 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
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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.
Received: 11.08.2008
English version:
Computational Mathematics and Mathematical Physics, 2009, Volume 49, Issue 9, Pages 1554–1566
DOI: https://doi.org/10.1134/S0965542509090103
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
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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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:73
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