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On the numerical solution of space–time fractional diffusion models

✍ Scribed by Emmanuel Hanert

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
892 KB
Volume
46
Category
Article
ISSN
0045-7930

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✦ Synopsis

A flexible numerical scheme for the discretization of the space-time fractional diffusion equation is presented. The model solution is discretized in time with a pseudo-spectral expansion of Mittag-Leffler functions. For the space discretization, the proposed scheme can accommodate either low-order finitedifference and finite-element discretizations or high-order pseudo-spectral discretizations. A number of examples of numerical solutions of the space-time fractional diffusion equation are presented with various combinations of the time and space derivatives. The proposed numerical scheme is shown to be both efficient and flexible.

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