A FRACTIONAL ANALOG OF CRANK–NICHOLSON METHOD FOR THE TWO SIDED SPACE FRACTIONAL PARTIAL EQUATION WITH FUNCTIONAL DELAY

Vladimir G. Pimenov     (Ural Federal University; Krasovskii Institute of Mathematics and Mechanics, Ekaterinburg, Russian Federation)
Ahmed S. Hendy     (Ural Federal University, Ekaterinburg, Russian Federation)

Abstract


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, Interpolation, Extrapolation, Convergence order

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References


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DOI: http://dx.doi.org/10.15826/umj.2016.1.005

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