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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 11, Page 1867
DOI: https://doi.org/10.31857/S0044466922110035 (Mi zvmmf11472) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Partial Differential Equations

Numerical solution of two and three-dimensional fractional heat conduction equations via Bernstein polynomials

M. Gholizadeh, M. Alipour, M. Behroozifar

Department of Mathematics, Faculty of Basic Science, Babol Noshirvani University of Technology, Shariati Ave, 47148-71167 Babol, Iran
Citations (2)
DOI: https://doi.org/10.31857/S0044466922110035
Abstract: In this paper, we develop a new scheme for the numerical solution of the two- and three-dimensional fractional heat conduction equations on a rectangular plane. Our main aim is to characterize the Bernstein operational matrices of derivative and integration in the two and three-dimensional cases and then apply them for solving the mentioned problems. This work causes to reduce the solution of fractional differential equations to the solution of an algebraic equation system. The presented method is applied to solve several problems. Approximated solutions are compared with the exact solutions which results show a negligible error.
Key words: Bernstein polynomials, two- and three-dimensional fractional heat conduction equations, operational matrices, Caputo fractional derivative, Riemann–Liouville fractional integral.
Received: 11.10.2021
Revised: 10.06.2022
Accepted: 07.07.2022
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 11, Pages 1865–1884
DOI: https://doi.org/10.1134/S0965542522110033
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: English
Citation: M. Gholizadeh, M. Alipour, M. Behroozifar, “Numerical solution of two and three-dimensional fractional heat conduction equations via Bernstein polynomials”, Zh. Vychisl. Mat. Mat. Fiz., 62:11 (2022), 1867; Comput. Math. Math. Phys., 62:11 (2022), 1865–1884
Citation in format AMSBIB
\Bibitem{GhoAliBeh22}
\by M.~Gholizadeh, M.~Alipour, M.~Behroozifar
\paper Numerical solution of two and three-dimensional fractional heat conduction equations via Bernstein polynomials
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 11
\pages 1867
\mathnet{http://mi.mathnet.ru/zvmmf11472}
\crossref{https://doi.org/10.31857/S0044466922110035}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4517578}
\elib{https://elibrary.ru/item.asp?id=49455080}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 11
\pages 1865--1884
\crossref{https://doi.org/10.1134/S0965542522110033}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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