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Finite difference methods for fractional dispersion equations. (English) Zbl 1193.65158
Summary: The fractional weighted average finite difference method for space-fractional advection-dispersion equation is proposed, which is based on shifted Grünwald formula. This method is unconditionally stable, consistent and convergent. A numerical example is given, and the numerical results verify the theoretical conclusions.
MSC:
65M06Finite difference methods (IVP of PDE)
35K20Second order parabolic equations, initial boundary value problems
35R11Fractional partial differential equations
65M12Stability and convergence of numerical methods (IVP of PDE)
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