Geodesic
Stability and convergence of difference schemes for boundary value problems for the fractional-order diffusion equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 4, pp. 572-586

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A family of difference schemes for the fractional-order diffusion equation with variable coefficients is considered. By the method of energetic inequalities, a priori estimates are obtained for solutions of finite-difference problems, which imply the stability and convergence of the difference schemes considered. The validity of the results is confirmed by numerical calculations for test examples. 
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     author = {A. A. Alikhanov},
     title = {Stability and convergence of difference schemes for boundary value problems for the fractional-order diffusion equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {572--586},
     publisher = {mathdoc},
     volume = {56},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_4_a4/}
}
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A. A. Alikhanov. Stability and convergence of difference schemes for boundary value problems for the fractional-order diffusion equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 4, pp. 572-586. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_4_a4/