Quartic spline method for solving second-order boundary value problems

Al-Said, EA; Noor, MA; Almualim, AH; Kokkinis, B; Coletsos, J

dc.contributor.author	Al-Said, EA	en
dc.contributor.author	Noor, MA	en
dc.contributor.author	Almualim, AH	en
dc.contributor.author	Kokkinis, B	en
dc.contributor.author	Coletsos, J	en
dc.date.accessioned	2014-03-01T02:03:10Z
dc.date.available	2014-03-01T02:03:10Z
dc.date.issued	2011	en
dc.identifier.issn	19921950	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29357
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-80053004256&partnerID=40&md5=02ce0f7e9a36dd27a07a574688d07f2e	en
dc.subject	Boundary value problems	en
dc.subject	Convergence analysis	en
dc.subject	Finite difference approximations	en
dc.subject	Quartic spline function	en
dc.title	Quartic spline method for solving second-order boundary value problems	en
heal.type	journalArticle	en
heal.publicationDate	2011	en
heal.abstract	In this paper, uniform quartic spline polynomial functions are used to develop some consistency relations which are then used to derive a numerical method for approximating the solution and its first, second, third and fourth derivatives of second order boundary value problems. The present method is capable of producing fourth order accurate approximations for the solution, as well as its first and second derivatives, and the second order accurate approximations for its third and fourth derivatives. The main consistency relation for the study's quartic spline method is the same relation derived by Usmani et al. (1987) using quartic spline function. Their spline method has a stability problem which affects the accuracy of the computed approximations, whereas for the study's new method, such stability problem does not appear. The present method produces more accurate approximations for the first and third derivatives of the solution than those produced by the other quartic spline method. A numerical example is included to demonstrate the efficiency and implementation of the proposed method. ©2011 Academic Journals.	en
heal.journalName	International Journal of Physical Sciences	en
dc.identifier.volume	6	en
dc.identifier.issue	17	en
dc.identifier.spage	4208	en
dc.identifier.epage	4212	en