Geodesic
Numerical Method of Value Boundary Problem Decision for 2D Equation of Heat Conductivity With Fractional Derivatives
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 5 (2010), pp. 244-251

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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. 
@article{VSGTU_2010_5_a26,
     author = {V. D. Beybalaev and M. R. Shabanova},
     title = {Numerical {Method} of {Value} {Boundary} {Problem} {Decision} for {2D} {Equation} of {Heat} {Conductivity} {With} {Fractional} {Derivatives}},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {244--251},
     publisher = {mathdoc},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2010_5_a26/}
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V. D. Beybalaev; M. R. Shabanova. Numerical Method of Value Boundary Problem Decision for 2D Equation of Heat Conductivity With Fractional Derivatives. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 5 (2010), pp. 244-251. http://geodesic.mathdoc.fr/item/VSGTU_2010_5_a26/