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dc.contributor.authorYan, yubin
dc.contributor.authorWang, Yanyong
dc.contributor.authorYan, Yuyuan
dc.contributor.authorPani, Amiya K.
dc.date.accessioned2020-06-11T08:43:10Z
dc.date.available2020-06-11T08:43:10Z
dc.date.issued2020-05-19
dc.identifierhttps://chesterrep.openrepository.com/bitstream/handle/10034/623491/Wang_yan_yan_pani-R2-final.pdf?sequence=1
dc.identifier.citationWang, Y., Yan, Y., Yan, Y. et al. (2020). Higher Order Time Stepping Methods for Subdiffusion Problems Based on Weighted and Shifted Grünwald–Letnikov Formulae with Nonsmooth Data. Journal of Scientific Computing, 83, 40.en_US
dc.identifier.doi10.1007/s10915-020-01223-y
dc.identifier.urihttp://hdl.handle.net/10034/623491
dc.description.abstractTwo higher order time stepping methods for solving subdiffusion problems are studied in this paper. The Caputo time fractional derivatives are approximated by using the weighted and shifted Gr\"unwald-Letnikov formulae introduced in Tian et al. [Math. Comp. 84 (2015), pp. 2703-2727]. After correcting a few starting steps, the proposed time stepping methods have the optimal convergence orders $O(k^2)$ and $ O(k^3)$, respectively for any fixed time $t$ for both smooth and nonsmooth data. The error estimates are proved by directly bounding the approximation errors of the kernel functions. Moreover, we also present briefly the applicabilities of our time stepping schemes to various other fractional evolution equations. Finally, some numerical examples are given to show that the numerical results are consistent with the proven theoretical results.en_US
dc.publisherSpringer Linken_US
dc.relation.urlhttps://link.springer.com/article/10.1007%2Fs10915-020-01223-y#citeasen_US
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en_US
dc.subjectweighted and shifted Gr$\ddot{u}$nwald -Letnikov formulaeen_US
dc.subjectsubdiffusion equationen_US
dc.subjectCaputo derivativeen_US
dc.subjectLaplace transformen_US
dc.subjecthigher order time stepping schemesen_US
dc.titleHigher Order Time Stepping Methods for Subdiffusion Problems Based on Weighted and Shifted Grünwald–Letnikov Formulae with Nonsmooth Dataen_US
dc.typeArticleen_US
dc.identifier.eissn1573-7691en_US
dc.contributor.departmentUniversity of Chester, Lvliang University, Jimei University, Indian Institute of Technology Bombayen_US
dc.identifier.journalJournal of Scientific Computingen_US
or.grant.openaccessYesen_US
rioxxterms.funderunfundeden_US
rioxxterms.identifier.projectunfundeden_US
rioxxterms.versionAMen_US
rioxxterms.versionofrecordhttps://doi.org/10.1007/s10915-020-01223-yen_US
rioxxterms.licenseref.startdate2021-05-19
refterms.dateFCD2020-06-10T16:10:29Z
refterms.versionFCDAM
rioxxterms.publicationdate2020-05-19
dc.dateAccepted2020-04-18
dc.date.deposited2020-06-11en_US
dc.indentifier.issn0885-7474en_US


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