Preprint No. A-03-05

E. A. Abdel-Rehim, Rudolf Gorenflo

Approximation of time-fractional diffusion with central drift by difference schemes

Abstract: By generalization of Ehrenfest's urn model, we obtain discrete approximations to spacially one-dimensional time fractional diffusion processes with drift towards the origin. These discrete approximations can be interpreted (a) as difference schemes for the relevant time-fractional partial differential equation, (b) as random walk models. The relevant convergence questions as well as the behaviour for time tending to infinity are discussed, and results of numerical case studies are displayed.

Keywords: generalization of Ehrenfest's urn model, diffusion processes with memory and central drift in a potential well, difference schemes, random walk models, fractional derivative, stochastic processes.

Mathematics Subject Classification (MSC2000): 26A33, 45K05, 60J60, 60G50, 65N06.

Language: ENG


Contact: Entsar Abdel-Rehim and Rudolf Gorenflo, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (,

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