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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 2, Pages 264–281 (Mi zvmmf182)  
This article is cited in 6 scientific papers (total in 6 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
Full-text PDF (2100 kB) Citations (6)
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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.
Received: 29.11.2005
Revised: 06.08.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 2, Pages 251–268
DOI: https://doi.org/10.1007/s11470-008-2008-0
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
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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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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