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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

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