A note on finite difference methods for nonlinear fractional differential equations with non-uniform meshes

Hdl Handle:
http://hdl.handle.net/10034/620595
Title:
A note on finite difference methods for nonlinear fractional differential equations with non-uniform meshes
Authors:
Yanzhi, Liu; Roberts, Jason; Yan, Yubin
Abstract:
We 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.
Affiliation:
Lvliang University; University of Chester
Citation:
Yanzhi, L., Roberts, J., & Yan, Y. (2017 - in press). A note on finite difference methods for nonlinear fractional differential equations with non-uniform meshes. International Journal of Computer Mathematics.
Publisher:
Taylor & Francis
Journal:
International Journal of Computer Mathematics
Publication Date:
2017
URI:
http://hdl.handle.net/10034/620595
Additional Links:
http://www.tandfonline.com/toc/gcom20/current
Type:
Article
Language:
en
EISSN:
1029-0265
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorYanzhi, Liuen
dc.contributor.authorRoberts, Jasonen
dc.contributor.authorYan, Yubinen
dc.date.accessioned2017-08-10T10:57:41Z-
dc.date.available2017-08-10T10:57:41Z-
dc.date.issued2017-
dc.identifier.citationYanzhi, L., Roberts, J., & Yan, Y. (2017 - in press). A note on finite difference methods for nonlinear fractional differential equations with non-uniform meshes. International Journal of Computer Mathematics.en
dc.identifier.urihttp://hdl.handle.net/10034/620595-
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.en
dc.language.isoenen
dc.publisherTaylor & Francisen
dc.relation.urlhttp://www.tandfonline.com/toc/gcom20/currenten
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 Mathematicsen
dc.date.accepted2017-07-28-
or.grant.openaccessYesen
rioxxterms.funderUnfundeden
rioxxterms.identifier.projectUnfundeden
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2217-08-10-
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