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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2012, Issue 2(27), Pages 183–187
DOI: https://doi.org/10.14498/vsgtu946 (Mi vsgtu946) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Short Communication
Mathematical Modelling

On the numerical solution of the Dirihlets problem for the Poisson's equation with fractional order derivatives

V. D. Beybalaev

Daghestan State University, Makhachkala, Russia
Full-text PDF (139 kB) Citations (4)
(published under the terms of the Creative Commons Attribution 4.0 International License)
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DOI: https://doi.org/10.14498/vsgtu946
Abstract: Difference approximation for the Caputo fractional derivative of the $4-\beta$, $1<\beta\leq 2$, order is obtained in the work. The difference schemes for solving the Dirichlet problem for the Poisson equation with fractional derivatives are developed. The right part and initial data stability of difference problem and its convergence are proved.
Keywords: Poisson's equation, Dirichlet problem, fractional order derivative, numerical method, approximation, difference problem.
Original article submitted 22/IV/2011
revision submitted – 12/XII/2011
Bibliographic databases:
Document Type: Article
UDC: 519.642.2:517.968.72
MSC: Primary 39A14; Secondary 35R11, 26A33, 45K05
Language: Russian
Citation: V. D. Beybalaev, “On the numerical solution of the Dirihlets problem for the Poisson's equation with fractional order derivatives”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(27) (2012), 183–187
Citation in format AMSBIB
\Bibitem{Bey12}
\by V.~D.~Beybalaev
\paper On the numerical solution of the Dirihlets problem for the Poisson's equation with fractional order derivatives
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2012
\vol 2(27)
\pages 183--187
\mathnet{http://mi.mathnet.ru/vsgtu946}
\crossref{https://doi.org/10.14498/vsgtu946}
\zmath{https://zbmath.org/?q=an:1326.39007}
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  • https://www.mathnet.ru/eng/vsgtu/v127/p183
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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    Full-text PDF :283
    References:75
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