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On the numerical solution of space-time fractional diffusion models. (English) Zbl 1305.65212
Summary: 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 finite-difference 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.

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
26A33 Fractional derivatives and integrals
33E12 Mittag-Leffler functions and generalizations
35R11 Fractional partial differential equations
45K05 Integro-partial differential equations
ma2dfc; mlrnd
Full Text: DOI
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