dc.contributor.author Yan, yubin dc.contributor.author Wang, Yanyong dc.contributor.author Yan, Yuyuan dc.contributor.author Pani, Amiya K. dc.date.accessioned 2020-06-11T08:43:10Z dc.date.available 2020-06-11T08:43:10Z dc.date.issued 2020-05-19 dc.identifier https://chesterrep.openrepository.com/bitstream/handle/10034/623491/Wang_yan_yan_pani-R2-final.pdf?sequence=1 dc.identifier.citation Wang, 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.doi 10.1007/s10915-020-01223-y dc.identifier.uri http://hdl.handle.net/10034/623491 dc.description.abstract Two higher order time stepping methods for solving subdiffusion problems are studied in this paper. en_US 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. dc.publisher Springer Link en_US dc.relation.url https://link.springer.com/article/10.1007%2Fs10915-020-01223-y#citeas en_US dc.rights.uri http://creativecommons.org/licenses/by/4.0/ en_US dc.subject weighted and shifted Gr\$\ddot{u}\$nwald -Letnikov formulae en_US dc.subject subdiffusion equation en_US dc.subject Caputo derivative en_US dc.subject Laplace transform en_US dc.subject higher order time stepping schemes en_US dc.title Higher Order Time Stepping Methods for Subdiffusion Problems Based on Weighted and Shifted Grünwald–Letnikov Formulae with Nonsmooth Data en_US dc.type Article en_US dc.identifier.eissn 1573-7691 en_US dc.contributor.department University of Chester, Lvliang University, Jimei University, Indian Institute of Technology Bombay en_US dc.identifier.journal Journal of Scientific Computing en_US or.grant.openaccess Yes en_US rioxxterms.funder unfunded en_US rioxxterms.identifier.project unfunded en_US rioxxterms.version AM en_US rioxxterms.versionofrecord https://doi.org/10.1007/s10915-020-01223-y en_US rioxxterms.licenseref.startdate 2021-05-19 refterms.dateFCD 2020-06-10T16:10:29Z refterms.versionFCD AM rioxxterms.publicationdate 2020-05-19 dc.dateAccepted 2020-04-18 dc.date.deposited 2020-06-11 en_US dc.indentifier.issn 0885-7474 en_US
﻿

### Files in this item

Name:
Wang_yan_yan_pani-R2-final.pdf
Embargo:
2021-05-19
Size:
380.9Kb
Format:
PDF
Request:
Main article