High-Order Numerical Methods for Solving Time Fractional Partial Differential Equations

Hdl Handle:
http://hdl.handle.net/10034/620273
Title:
High-Order Numerical Methods for Solving Time Fractional Partial Differential Equations
Authors:
Li, Zhiqiang; Liang, Zongqi; Yan, Yubin
Abstract:
In 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.
Affiliation:
Luliang University, P. R. China, Jimei University, P. R. China, University of Chester, UK
Citation:
Li, Z., Liang, Z. & Yan, Y. (2016). High-order numerical methods for solving time fractional partial differential equations. Journal of Scientific Computing. DOI: 10.1007/s10915-016-0319-1
Publisher:
Springer Link
Journal:
Journal of Scientific Computing
Publication Date:
15-Nov-2016
URI:
http://hdl.handle.net/10034/620273
DOI:
10.1007/s10915-016-0319-1
Additional Links:
http://link.springer.com/article/10.1007/s10915-016-0319-1
Type:
Article
Language:
en
Description:
The final publication is available at Springer via http://dx.doi.org/10.1007/s10915-016-0319-1
ISSN:
0885-7474
EISSN:
1573-7691
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorLi, Zhiqiangen
dc.contributor.authorLiang, Zongqien
dc.contributor.authorYan, Yubinen
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. (2016). High-order numerical methods for solving time fractional partial differential equations. Journal of Scientific Computing. 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<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.en
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 Computingen
dc.date.accepted2016-11-01-
or.grant.openaccessYesen
rioxxterms.funderunfunded researchen
rioxxterms.identifier.projectunfunded researchen
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2017-11-15-
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