An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data

Hdl Handle:
http://hdl.handle.net/10034/620610
Title:
An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data
Authors:
Ford, Neville J.; Yan, Yubin
Abstract:
In this paper, we shall review an approach by which we can seek higher order time discretisation schemes for solving time fractional partial differential equations with nonsmooth data. The low regularity of the solutions of time fractional partial differential equations implies standard time discretisation schemes only yield first order accuracy. To obtain higher order time discretisation schemes when the solutions of time fractional partial differential equations have low regularities, one may correct the starting steps of the standard time discretisation schemes to capture the singularities of the solutions. We will consider these corrections of some higher order time discretisation schemes obtained by using Lubich's fractional multistep methods, L1 scheme and its modification, discontinuous Galerkin methods, etc. Numerical examples are given to show that the theoretical results are consistent with the numerical results.
Affiliation:
University of Chester
Citation:
Ford, N. J. & Yan, Y. (2017-forthcoming). An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data. Fractional Calculus and Applied Analysis.
Publisher:
De Gruyter
Journal:
Fractional Calculus and Applied Analysis - Fract. Calc. Appl. Anal
Publication Date:
Sep-2017
URI:
http://hdl.handle.net/10034/620610
Type:
Article
Language:
en
Description:
Invited review article for Anniversary Edition of Journal.
ISSN:
1314-2224
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorFord, Neville J.en
dc.contributor.authorYan, Yubinen
dc.date.accessioned2017-09-06T13:21:13Z-
dc.date.available2017-09-06T13:21:13Z-
dc.date.issued2017-09-
dc.identifier.citationFord, N. J. & Yan, Y. (2017-forthcoming). An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data. Fractional Calculus and Applied Analysis.en
dc.identifier.issn1314-2224-
dc.identifier.urihttp://hdl.handle.net/10034/620610-
dc.descriptionInvited review article for Anniversary Edition of Journal.en
dc.description.abstractIn this paper, we shall review an approach by which we can seek higher order time discretisation schemes for solving time fractional partial differential equations with nonsmooth data. The low regularity of the solutions of time fractional partial differential equations implies standard time discretisation schemes only yield first order accuracy. To obtain higher order time discretisation schemes when the solutions of time fractional partial differential equations have low regularities, one may correct the starting steps of the standard time discretisation schemes to capture the singularities of the solutions. We will consider these corrections of some higher order time discretisation schemes obtained by using Lubich's fractional multistep methods, L1 scheme and its modification, discontinuous Galerkin methods, etc. Numerical examples are given to show that the theoretical results are consistent with the numerical results.en
dc.language.isoenen
dc.publisherDe Gruyteren
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectfractional calculusen
dc.subjectnumerical schemesen
dc.titleAn approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth dataen
dc.typeArticleen
dc.contributor.departmentUniversity of Chesteren
dc.identifier.journalFractional Calculus and Applied Analysis - Fract. Calc. Appl. Analen
dc.date.accepted2017-08-27-
or.grant.openaccessYesen
rioxxterms.fundernoneen
rioxxterms.identifier.projectunfunded researchen
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2018-12-31-
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