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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.

MSC:
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
Software:
ma2dfc; mlrnd
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