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dc.contributor.authorYanzhi, Liu*
dc.contributor.authorRoberts, Jason A.*
dc.contributor.authorYan, Yubin*
dc.date.accessioned2017-08-10T10:57:41Z
dc.date.available2017-08-10T10:57:41Z
dc.date.issued2017-10-09
dc.identifier.citationYanzhi, L., Roberts, J., & Yan, Y. (2018). A note on finite difference methods for nonlinear fractional differential equations with non-uniform meshes. International Journal of Computer Mathematics, 95(6-7), 1151-1169. http://dx.doi.org/10.1080/00207160.2017.1381691en
dc.identifier.doi10.1080/00207160.2017.1381691
dc.identifier.urihttp://hdl.handle.net/10034/620595
dc.descriptionThis is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Computer Mathematics on 09/10/2017, available online: http://dx.doi.org/10.1080/00207160.2017.1381691
dc.description.abstractWe consider finite difference methods for solving nonlinear fractional differential equations in the Caputo fractional derivative sense with non-uniform meshes. Under the assumption that the Caputo derivative of the solution of the fractional differential equation is suitably smooth, Li et al. \lq \lq Finite difference methods with non-uniform meshes for nonlinear fractional differential equations\rq\rq, Journal of Computational Physics, 316(2016), 614-631, obtained the error estimates of finite difference methods with non-uniform meshes. However the Caputo derivative of the solution of the fractional differential equation in general has a weak singularity near the initial time. In this paper, we obtain the error estimates of finite difference methods with non-uniform meshes when the Caputo fractional derivative of the solution of the fractional differential equation has lower smoothness. The convergence result shows clearly how the regularity of the Caputo fractional derivative of the solution affect the order of convergence of the finite difference methods. Numerical results are presented that confirm the sharpness of the error analysis.
dc.language.isoenen
dc.publisherTaylor & Francisen
dc.relation.urlhttps://www.tandfonline.com/doi/full/10.1080/00207160.2017.1381691en
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subjectNonlinear fractional differential equationen
dc.subjectPredictor-corrector methoden
dc.subjectError estimatesen
dc.subjectNon-uniform meshesen
dc.subjectTrapezoid formulaen
dc.titleA note on finite difference methods for nonlinear fractional differential equations with non-uniform meshesen
dc.typeArticleen
dc.identifier.eissn1029-0265
dc.contributor.departmentLvliang University; University of Chesteren
dc.identifier.journalInternational Journal of Computer Mathematics
dc.date.accepted2017-07-28
or.grant.openaccessYesen
rioxxterms.funderUnfundeden
rioxxterms.identifier.projectUnfundeden
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2018-10-09
refterms.dateFCD2019-07-15T09:55:35Z
refterms.versionFCDAM
refterms.dateFOA2018-10-09T00:00:00Z
html.description.abstractWe consider finite difference methods for solving nonlinear fractional differential equations in the Caputo fractional derivative sense with non-uniform meshes. Under the assumption that the Caputo derivative of the solution of the fractional differential equation is suitably smooth, Li et al. \lq \lq Finite difference methods with non-uniform meshes for nonlinear fractional differential equations\rq\rq, Journal of Computational Physics, 316(2016), 614-631, obtained the error estimates of finite difference methods with non-uniform meshes. However the Caputo derivative of the solution of the fractional differential equation in general has a weak singularity near the initial time. In this paper, we obtain the error estimates of finite difference methods with non-uniform meshes when the Caputo fractional derivative of the solution of the fractional differential equation has lower smoothness. The convergence result shows clearly how the regularity of the Caputo fractional derivative of the solution affect the order of convergence of the finite difference methods. Numerical results are presented that confirm the sharpness of the error analysis.
rioxxterms.publicationdate2017-10-09


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