Finite Difference Method for Two-Sided Space-Fractional Partial Differential Equations
AffiliationUniversity of Chester
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AbstractFinite difference methods for solving two-sided space-fractional partial differential equations are studied. The space-fractional derivatives are the left-handed and right-handed Riemann-Liouville fractional derivatives which are expressed by using Hadamard finite-part integrals. The Hadamard finite-part integrals are approximated by using piecewise quadratic interpolation polynomials and a numerical approximation scheme of the space-fractional derivative with convergence order O(Δx^(3−α )),10 , where Δt,Δx denote the time and space step sizes, respectively. Numerical examples are presented and compared with the exact analytical solution for its order of convergence.
CitationPal, K., Liu, F., Yan, Y. & Roberts, G. (2015). Finite difference method for two-sided space-fractional partial differential equations. In I. Dimov, I. Farago & L. Vulkov (Eds.), Finite difference methods, theory and applications. 6th International Conference, FDM 2014 (pp. 307-314). Springer.
PublisherSpringer International Publishing
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