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dc.contributor.authorLi, Zhiqiang*
dc.contributor.authorLiang, Zongqi*
dc.contributor.authorYan, Yubin*
dc.date.accessioned2016-12-02T11:59:24Z
dc.date.available2016-12-02T11:59:24Z
dc.date.issued2016-11-15
dc.identifier.citationLi, Z., Liang, Z. & Yan, Y. (2017). High-order numerical methods for solving time fractional partial differential equations. Journal of Scientific Computing, 71(2), 785-803. DOI: 10.1007/s10915-016-0319-1en
dc.identifier.issn0885-7474
dc.identifier.doi10.1007/s10915-016-0319-1
dc.identifier.urihttp://hdl.handle.net/10034/620273
dc.descriptionThe final publication is available at Springer via http://dx.doi.org/10.1007/s10915-016-0319-1en
dc.description.abstractIn this paper we introduce a new numerical method for solving time fractional partial differential equation. The time discretization is based on Diethelm’s method where the Hadamard finite-part integral is approximated by using the piecewise quadratic interpolation polynomials. The space discretization is based on the standard finite element method. The error estimates with the convergence order O(τ^(3−α) +h^2 ),0
dc.language.isoenen
dc.publisherSpringer Linken
dc.relation.urlhttp://link.springer.com/article/10.1007/s10915-016-0319-1en
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjecttime fractional partial differential equationsen
dc.subjectfinite element methoden
dc.subjecterror estimatesen
dc.titleHigh-Order Numerical Methods for Solving Time Fractional Partial Differential Equationsen
dc.typeArticleen
dc.identifier.eissn1573-7691
dc.contributor.departmentLuliang University, P. R. China, Jimei University, P. R. China, University of Chester, UKen
dc.identifier.journalJournal of Scientific Computing
dc.date.accepted2016-11-01
or.grant.openaccessYesen
rioxxterms.funderunfunded researchen
rioxxterms.identifier.projectunfunded researchen
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2017-11-15
refterms.dateFCD2019-07-15T09:55:37Z
refterms.versionFCDAM
refterms.dateFOA2017-11-15T00:00:00Z
html.description.abstractIn this paper we introduce a new numerical method for solving time fractional partial differential equation. The time discretization is based on Diethelm’s method where the Hadamard finite-part integral is approximated by using the piecewise quadratic interpolation polynomials. The space discretization is based on the standard finite element method. The error estimates with the convergence order O(τ^(3−α) +h^2 ),0<α<1 O(τ^(3−α)+h^2),0<α<1 are proved in detail by using the argument developed recently by Lv and Xu (SIAM J Sci Comput 38:A2699–A2724, 2016), where τ and h denote the time and space step sizes, respectively. Numerical examples in both one- and two-dimensional cases are given.


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