Error estimates of a high order numerical method for solving linear fractional differential equations

Hdl Handle:
http://hdl.handle.net/10034/609518
Title:
Error estimates of a high order numerical method for solving linear fractional differential equations
Authors:
Li, Zhiqiang; Yan, Yubin; Ford, Neville J.
Abstract:
In this paper, we first introduce an alternative proof of the error estimates of the numerical methods for solving linear fractional differential equations proposed in Diethelm [6] where a first-degree compound quadrature formula was used to approximate the Hadamard finite-part integral and the convergence order of the proposed numerical method is O(∆t 2−α ), 0 < α < 1, where α is the order of the fractional derivative and ∆t is the step size. We then use the similar idea to prove the error estimates of a high order numerical method for solving linear fractional differential equations proposed in Yan et al. [37], where a second-degree compound quadrature formula was used to approximate the Hadamard finite-part integral and we show that the convergence order of the numerical method is O(∆t 3−α ), 0 < α < 1. The numerical examples are given to show that the numerical results are consistent with the theoretical results.
Affiliation:
Luliang University; University of Chester
Citation:
Li, Z., Yan, Y., & Ford, N. J. (2016). Error estimates of a high order numerical method for solving linear fractional differential equations. Applied Numerical Mathematics, 114, 201-220. DOI: 10.1016/j.apnum.2016.04.010
Publisher:
Elsevier, IMACS
Journal:
Applied Numerical Mathematics
Publication Date:
29-Apr-2016
URI:
http://hdl.handle.net/10034/609518
DOI:
10.1016/j.apnum.2016.04.010
Additional Links:
http://www.journals.elsevier.com/applied-numerical-mathematics/
Type:
Article
Language:
en
EISSN:
1873-5460
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorLi, Zhiqiangen
dc.contributor.authorYan, Yubinen
dc.contributor.authorFord, Neville J.en
dc.date.accessioned2016-05-17T08:50:28Zen
dc.date.available2016-05-17T08:50:28Zen
dc.date.issued2016-04-29en
dc.identifier.citationLi, Z., Yan, Y., & Ford, N. J. (2016). Error estimates of a high order numerical method for solving linear fractional differential equations. Applied Numerical Mathematics, 114, 201-220. DOI: 10.1016/j.apnum.2016.04.010en
dc.identifier.doi10.1016/j.apnum.2016.04.010-
dc.identifier.urihttp://hdl.handle.net/10034/609518en
dc.description.abstractIn this paper, we first introduce an alternative proof of the error estimates of the numerical methods for solving linear fractional differential equations proposed in Diethelm [6] where a first-degree compound quadrature formula was used to approximate the Hadamard finite-part integral and the convergence order of the proposed numerical method is O(∆t 2−α ), 0 < α < 1, where α is the order of the fractional derivative and ∆t is the step size. We then use the similar idea to prove the error estimates of a high order numerical method for solving linear fractional differential equations proposed in Yan et al. [37], where a second-degree compound quadrature formula was used to approximate the Hadamard finite-part integral and we show that the convergence order of the numerical method is O(∆t 3−α ), 0 < α < 1. The numerical examples are given to show that the numerical results are consistent with the theoretical results.en
dc.language.isoenen
dc.publisherElsevier, IMACSen
dc.relation.urlhttp://www.journals.elsevier.com/applied-numerical-mathematics/en
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectFractional calculusen
dc.subjectNumerical methodsen
dc.titleError estimates of a high order numerical method for solving linear fractional differential equationsen
dc.typeArticleen
dc.identifier.eissn1873-5460en
dc.contributor.departmentLuliang University; University of Chesteren
dc.identifier.journalApplied Numerical Mathematicsen
dc.date.accepted2016-04-24en
or.grant.openaccessYesen
rioxxterms.funderUnfundeden
rioxxterms.identifier.projectUnfundeden
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2017-05-01en
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