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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.publisherSpringer International Publishingen
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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