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 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]: Year: Volume: Issue: Page: Find

 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2010, Issue 5(21), Pages 244–251 (Mi vsgtu776)

Calculus Mathematics

Numerical Method of Value Boundary Problem Decision for 2D Equation of Heat Conductivity With Fractional Derivatives

V. D. Beybalaeva, M. R. Shabanovab

a Dept. of Applied Mathematics, Daghestan State University, Makhachkala
b Lab. of Mathematical Modeling and Monitoring of Geothermal Objects, Institute of Geothermy Problems, Dagestan Research Center of RAS, Makhachkala

Abstract: In this work a solution is obtained for the boundary problem for two-dimensional thermal conductivity equation with derivatives of fractional order on time and space variables by grid method. Explicit and implicit difference schemes are developed. Stability criteria of these difference schemes are proven. It is shown that approximation order by time equal but by space variables it equal two. A solution method is suggested using fractional steps. It is proved that the transition module, corresponding to two half-steps, approximates the transition module for given equation.

Keywords: numerical methods, stability, approximation of fractional derivatives, fractional differential equations

DOI: https://doi.org/10.14498/vsgtu776

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Bibliographic databases:

UDC: 517.98
MSC: Primary 65N12; Secondary 34A08, 26A33, 45K05
Original article submitted 08/II/2010
revision submitted – 28/IV/2010

Citation: V. D. Beybalaev, M. R. Shabanova, “Numerical Method of Value Boundary Problem Decision for 2D Equation of Heat Conductivity With Fractional Derivatives”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 5(21) (2010), 244–251

Citation in format AMSBIB
\Bibitem{BeySha10} \by V.~D.~Beybalaev, M.~R.~Shabanova \paper Numerical Method of Value Boundary Problem Decision for 2D Equation of Heat Conductivity With Fractional Derivatives \jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.] \yr 2010 \vol 5(21) \pages 244--251 \mathnet{http://mi.mathnet.ru/vsgtu776} \crossref{https://doi.org/10.14498/vsgtu776} 

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1. E. I. Abduragimov, R. A. Omarova, “Chislennyi metod postroeniya polozhitelnogo resheniya dvukhtochechnoi kraevoi zadachi dlya odnogo differentsialnogo uravneniya vtorogo poryadka s drobnoi proizvodnoi”, Vestnik Dagestanskogo gosudarstvennogo universiteta, 2014, no. 6, 40–46
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