A nonpolynomial collocation method for fractional terminal value problems

Ford, Neville J.; Morgado, Maria L.; Rebelo, Magda S.

dc.contributor.author	Ford, Neville J.	*
dc.contributor.author	Morgado, Maria L.	*
dc.contributor.author	Rebelo, Magda S.	*
dc.date.accessioned	2014-06-24T12:52:54Z
dc.date.available	2014-06-24T12:52:54Z
dc.date.issued	2014-06-14
dc.identifier.citation	Journal of Computational and Applied Mathematics, February 2015, 275, pp. 392-402	en
dc.identifier.issn	0377-0427	en
dc.identifier.doi	10.1016/j.cam.2014.06.013
dc.identifier.uri	http://hdl.handle.net/10034/322216
dc.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	en
dc.description.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.
dc.description.sponsorship	The work was supported by an International Research Excellence Award funded through the Santander Universities scheme.	en
dc.language.iso	en	en
dc.publisher	Elsevier	en
dc.relation.url	http://www.journals.elsevier.com/journal-of-computational-and-applied-mathematics/	en
dc.subject	numerical analysis	en
dc.subject	computational and mathematical modelling	en
dc.title	A nonpolynomial collocation method for fractional terminal value problems	en
dc.type	Article	en
dc.contributor.department	University of Chester ; UTAD, Portugal; Universidade de Nova Lisboa, Portugal	en
dc.identifier.journal	Journal of Computational and Applied Mathematics
html.description.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.
rioxxterms.publicationdate	2014-06-14