Equivalence and convergence of direct and indirect methods for the numerical solution of singular integral equations

Tsamasphyros, G; Theocaris, PS

dc.contributor.author	Tsamasphyros, G	en
dc.contributor.author	Theocaris, PS	en
dc.date.accessioned	2014-03-01T01:05:54Z
dc.date.available	2014-03-01T01:05:54Z
dc.date.issued	1981	en
dc.identifier.issn	0010-485X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/9069
dc.subject	Direct Method	en
dc.subject	Functional Equation	en
dc.subject	Linear System of Equations	en
dc.subject	Numerical Integration	en
dc.subject	Numerical Solution	en
dc.subject	Singular Integral Equation	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.other	MATHEMATICAL TECHNIQUES	en
dc.title	Equivalence and convergence of direct and indirect methods for the numerical solution of singular integral equations	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/BF02243439	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF02243439	en
heal.language	English	en
heal.publicationDate	1981	en
heal.abstract	Direct methods for solving Cauchy-type singular integral equations (S.I.E.) are based on Gauss numerical integration rule [1] where the S.I.E. is reduced to a linear system of equations by applying the resulting functional equation at properly selected collocation points. The equivalence of this formulation with the one based on the Lagrange interpolatory approximation of the unknown function was shown in the paper. Indirect methods for the solution of S. I. E. may be obtained after a reduction of it to an equivalent Fredholm integral equation and an application of the same numerical technique to the latter. It was shown in this paper that both methods are equivalent in the sense that they give the same numerical results. Using these results the error estimate and the convergence of the methods was established. © 1981 Springer-Verlag.	en
heal.publisher	Springer-Verlag	en
heal.journalName	Computing	en
dc.identifier.doi	10.1007/BF02243439	en
dc.identifier.isi	ISI:A1981LZ06300006	en
dc.identifier.volume	27	en
dc.identifier.issue	1	en
dc.identifier.spage	71	en
dc.identifier.epage	80	en