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This article is cited in 2 scientific papers (total in 2 papers)
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
(published under the terms of the Creative Commons Attribution 4.0 International License)
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.
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
Linking options:
https://www.mathnet.ru/eng/vsgtu776 https://www.mathnet.ru/eng/vsgtu/v121/p244
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