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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:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35R11 Fractional partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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