A nonpolynomial collocation method for fractional terminal value problems

Hdl Handle:
http://hdl.handle.net/10034/322216
Title:
A nonpolynomial collocation method for fractional terminal value problems
Authors:
Ford, Neville J.; Morgado, Maria L.; Rebelo, Magda S.
Abstract:
In this paper we propose a non-polynomial collocation method for solving a class of terminal (or boundary) value problems for differential equations of fractional order α, 0 < α < 1. The approach used is based on the equivalence between a problem of this type and a Fredholm integral equation of a particular form. Taking into account the asymptotic behaviour of the solution of this problem, we propose a non-polynomial collocation method on a uniform mesh. We study the order of convergence of the proposed algorithm and a result on optimal order of convergence is obtained. In order to illustrate the theoretical results and the performance of the method we present several numerical examples.
Affiliation:
University of Chester ; UTAD, Portugal; Universidade de Nova Lisboa, Portugal
Citation:
Journal of Computational and Applied Mathematics, February 2015, 275, pp. 392-402
Publisher:
Elsevier
Journal:
Journal of Computational and Applied Mathematics
Publication Date:
24-Jun-2014
URI:
http://hdl.handle.net/10034/322216
DOI:
10.1016/j.cam.2014.06.013
Additional Links:
http://www.journals.elsevier.com/journal-of-computational-and-applied-mathematics/
Type:
Article
Language:
en
Description:
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational and Applied Mathematics, 275, February 2015, doi: 10.1016/j.cam.2014.06.013
ISSN:
0377-0427
Sponsors:
The work was supported by an International Research Excellence Award funded through the Santander Universities scheme.
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorFord, Neville J.en
dc.contributor.authorMorgado, Maria L.en
dc.contributor.authorRebelo, Magda S.en
dc.date.accessioned2014-06-24T12:52:54Zen
dc.date.available2014-06-24T12:52:54Zen
dc.date.issued2014-06-24en
dc.identifier.citationJournal of Computational and Applied Mathematics, February 2015, 275, pp. 392-402en
dc.identifier.issn0377-0427en
dc.identifier.doi10.1016/j.cam.2014.06.013en
dc.identifier.urihttp://hdl.handle.net/10034/322216en
dc.descriptionNOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational and Applied Mathematics, 275, February 2015, doi: 10.1016/j.cam.2014.06.013en
dc.description.abstractIn this paper we propose a non-polynomial collocation method for solving a class of terminal (or boundary) value problems for differential equations of fractional order α, 0 < α < 1. The approach used is based on the equivalence between a problem of this type and a Fredholm integral equation of a particular form. Taking into account the asymptotic behaviour of the solution of this problem, we propose a non-polynomial collocation method on a uniform mesh. We study the order of convergence of the proposed algorithm and a result on optimal order of convergence is obtained. In order to illustrate the theoretical results and the performance of the method we present several numerical examples.en
dc.description.sponsorshipThe work was supported by an International Research Excellence Award funded through the Santander Universities scheme.en
dc.language.isoenen
dc.publisherElsevieren
dc.relation.urlhttp://www.journals.elsevier.com/journal-of-computational-and-applied-mathematics/en
dc.subjectnumerical analysisen
dc.subjectcomputational and mathematical modellingen
dc.titleA nonpolynomial collocation method for fractional terminal value problemsen
dc.typeArticleen
dc.contributor.departmentUniversity of Chester ; UTAD, Portugal; Universidade de Nova Lisboa, Portugalen
dc.identifier.journalJournal of Computational and Applied Mathematicsen
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