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dc.contributor.authorPal, Kamal*
dc.contributor.authorLiu, Fang*
dc.contributor.authorYan, Yubin*
dc.contributor.authorRoberts, Graham*
dc.date.accessioned2015-11-17T09:33:56Z
dc.date.available2015-11-17T09:33:56Z
dc.date.issued2015-06-17
dc.identifier.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.en
dc.identifier.isbn9783319202396en
dc.identifier.urihttp://hdl.handle.net/10034/582252
dc.description.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.
dc.language.isoenen
dc.publisherSpringeren
dc.relation.urlhttp://www.springer.com/gp/book/9783319202389en
dc.subjectFinite difference methoden
dc.subjectspace-fractional partial differential equationsen
dc.subjecterror estimatesen
dc.subjectstabilityen
dc.titleFinite Difference Method for Two-Sided Space-Fractional Partial Differential Equationsen
dc.typeBook chapteren
dc.contributor.departmentUniversity of Chesteren
html.description.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 )),1<α<2 is obtained. A shifted implicit finite difference method is introduced for solving two-sided space-fractional partial differential equation and we prove that the order of convergence of the finite difference method is O(Δt+Δx^( min(3−α,β)) ),1<α<2,β>0 , 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.
rioxxterms.publicationdate2015-06-17


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