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Finite difference method for Riesz space fractional advection-dispersion equation with fractional Robin boundary condition. (English) Zbl 1474.65281

Summary: In this paper, a Riesz space fractional advection-dispersion equation with fractional Robin boundary condition is considered. By applying the fractional central difference formula and the weighted and shifted Grunwald-Letnikov formula, we derive a weighted implicit finite difference scheme with accuracy \(O (\Delta {t^2} + {h^2})\). The solvability, stability, and convergence of the proposed numerical scheme are proved. A numerical example is presented to confirm the accuracy and efficiency of the scheme.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
26A33 Fractional derivatives and integrals
35R11 Fractional partial differential equations
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