TREATMENT OF THE POLE AT INFINITY IN CLASSICAL NUMERICAL-INTEGRATION WITH COMPUTER ALGEBRA SOFTWARE

IOAKIMIDIS, NI; ANASTASSELOS, GT

dc.contributor.author	IOAKIMIDIS, NI	en
dc.contributor.author	ANASTASSELOS, GT	en
dc.date.accessioned	2014-03-01T01:42:16Z
dc.date.available	2014-03-01T01:42:16Z
dc.date.issued	1993	en
dc.identifier.issn	0020-7160	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/23743
dc.subject	ANALYTIC FUNCTIONS	en
dc.subject	ASYMPTOTIC SERIES EXPANSIONS	en
dc.subject	COMPUTER ALGEBRA SOFTWARE	en
dc.subject	CONTOUR INTEGRALS	en
dc.subject	ERROR TERM	en
dc.subject	EXPANSIONS	en
dc.subject	GAUSS-CHEBYSHEV RULE	en
dc.subject	GAUSS-LEGENDRE RULE	en
dc.subject	NUMERICAL INTEGRATION	en
dc.subject	POLES	en
dc.subject	PRINCIPAL VALUE INTEGRALS	en
dc.subject	QUADRATURE RULES	en
dc.subject	TAYLOR-MACLAURIN SERIES EXPANSIONS	en
dc.subject.classification	Mathematics, Applied	en
dc.title	TREATMENT OF THE POLE AT INFINITY IN CLASSICAL NUMERICAL-INTEGRATION WITH COMPUTER ALGEBRA SOFTWARE	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1993	en
heal.abstract	The error in the classical interpolatory (including Gaussian) numerical integration rules for analytic functions can be considered to be due to a 'pole' at infinity. The residue of this 'pole' is approximately taken into account by using Taylor-Maclaurin series expansions at the origin and asymptotic expansions at infinity. The computer algebra system Maple V was found appropriate and used in this task. The cases of the Gauss-Chebyshev and the Gauss-Legendre quadrature rules were considered in some detail. Finally, numerical results in applications both for regular and for Cauchy-type principal value integrals are also presented and the strong improvement in the numerical results by the present approach is illustrated.	en
heal.publisher	GORDON BREACH SCI PUBL LTD	en
heal.journalName	INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS	en
dc.identifier.isi	ISI:A1993NE95500010	en
dc.identifier.volume	49	en
dc.identifier.issue	1-2	en
dc.identifier.spage	75	en
dc.identifier.epage	83	en