Finite Difference Method for Two-Sided Space-Fractional Partial Differential Equations

Hdl Handle:
http://hdl.handle.net/10034/582252
Title:
Finite Difference Method for Two-Sided Space-Fractional Partial Differential Equations
Authors:
Pal, Kamal; Liu, Fang; Yan, Yubin; Roberts, Graham
Abstract:
Finite 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.
Affiliation:
University of Chester
Citation:
Pal, 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.
Publisher:
Springer International Publishing
Publication Date:
Jun-2015
URI:
http://hdl.handle.net/10034/582252
Additional Links:
http://www.springer.com/gp/book/9783319202389
Type:
Book chapter
Language:
en
ISBN:
978-3-319-20239-6
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorPal, Kamalen
dc.contributor.authorLiu, Fangen
dc.contributor.authorYan, Yubinen
dc.contributor.authorRoberts, Grahamen
dc.date.accessioned2015-11-17T09:33:56Zen
dc.date.available2015-11-17T09:33:56Zen
dc.date.issued2015-06en
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.isbn978-3-319-20239-6en
dc.identifier.urihttp://hdl.handle.net/10034/582252en
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 )),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.en
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
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