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A second order explicit finite difference method for the fractional advection diffusion equation. (English) Zbl 1268.65118
Summary: We develop a numerical method for fractional advection diffusion problems with source terms in domains with homogeneous boundary conditions. The numerical method is derived by using a Lax-Wendroff-type time discretization procedure, it is explicit and second order accurate. The convergence of the numerical method is studied and numerical results are presented.

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations
45K05 Integro-partial differential equations
Full Text: DOI
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