Geodesic
Fractional analog of crank-nicholson method for the two sided space fractional partial equation with functional delay
Ural mathematical journal, Tome 2 (2016) no. 1, pp. 48-57

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For two sided space fractional diffusion equation with time functional after-effect, an implicit numerical method is constructed and the order of its convergence is obtained. The method is a fractional analogue of the Crank-Nicholson method, and also uses interpolation and extrapolation of the prehistory of model with respect to time.
Keywords: Fractional partial differential equation, Grunwald-Letnikov approximations, Grid schemes, Functional delay
Mots-clés : Interpolation, Extrapolation, Convergence order. 
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     author = {Vladimir G. Pimenov and Ahmed S. Hendy},
     title = {Fractional analog of crank-nicholson method for the two sided space fractional partial equation with functional delay},
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     url = {http://geodesic.mathdoc.fr/item/UMJ_2016_2_1_a4/}
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Vladimir G. Pimenov; Ahmed S. Hendy. Fractional analog of crank-nicholson method for the two sided space fractional partial equation with functional delay. Ural mathematical journal, Tome 2 (2016) no. 1, pp. 48-57. http://geodesic.mathdoc.fr/item/UMJ_2016_2_1_a4/