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
Available: Pr-A-03-05.ps
Contact: Entsar Abdel-Rehim and Rudolf Gorenflo, Freie
Universität Berlin, Fachbereich Mathematik und Informatik,
Arnimallee 2-6, D-14195 Berlin, Germany (entsar@math.fu-berlin.de,
gorenflo@math.fu-berlin.de)
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