An error bound for approximate solutions of two-point boundary value problems

Kioustelidis, JB

dc.contributor.author	Kioustelidis, JB	en
dc.date.accessioned	2014-03-01T01:07:23Z
dc.date.available	2014-03-01T01:07:23Z
dc.date.issued	1989	en
dc.identifier.issn	0010-485X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/9962
dc.subject	AMS Subject Classification: 65L10	en
dc.subject	Elliptic boundary value problems	en
dc.subject	error bounds	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.title	An error bound for approximate solutions of two-point boundary value problems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/BF02239753	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF02239753	en
heal.language	English	en
heal.publicationDate	1989	en
heal.abstract	A new error bound for any approximate solution u of the two-point boundary value problem Ay:=-(py′)′+qy=f, y(0)=0, y(1)=0, is proposed. This error bound depends on the deviation Au-fjust like the one which is proportional to {norm of matrix}Au-f{norm of matrix}2, but in the case of Ritz-Galerkin approximations by cubic splines it behaves asymptotically like h3, where h is the knot distance, i.e., it is by one order of magnitude better. An important advantage of this error bound is that it can be used even in the case of generalized solutions and of piecewise linear approximations. An error bound for the approximation of the derivative results also from these considerations. This error bound behaves in the above case asymptotically also like h3, i.e. it has the same asymptotic behaviour as the actual approximation error of the derivative. © 1989 Springer-Verlag.	en
heal.publisher	Springer-Verlag	en
heal.journalName	Computing	en
dc.identifier.doi	10.1007/BF02239753	en
dc.identifier.isi	ISI:A1989AP09900013	en
dc.identifier.volume	42	en
dc.identifier.issue	2-3	en
dc.identifier.spage	259	en
dc.identifier.epage	270	en