Lin, Haixin; Fang, Shaomei Finite difference method for Riesz space fractional advection-dispersion equation with fractional Robin boundary condition. (English) Zbl 1474.65281 Chin. Q. J. Math. 35, No. 3, 278-289 (2020). 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. Cited in 1 Document 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 Keywords:fractional advection-dispersion equation; Riesz fractional derivative; fractional central difference; stability; convergence PDFBibTeX XMLCite \textit{H. Lin} and \textit{S. Fang}, Chin. Q. J. Math. 35, No. 3, 278--289 (2020; Zbl 1474.65281) Full Text: DOI