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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.

##### MSC:
 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
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