A method of numerical solution of cauchy-type singular integral equations with generalized kernels and arbitrary complex singularities

Theocaris, PS; Ioakimidis, NI

dc.contributor.author	Theocaris, PS	en
dc.contributor.author	Ioakimidis, NI	en
dc.date.accessioned	2014-03-01T01:37:58Z
dc.date.available	2014-03-01T01:37:58Z
dc.date.issued	1979	en
dc.identifier.issn	00219991	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/21877
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0000973212&partnerID=40&md5=9751bd144acd1957b83a45857780ff3b	en
dc.title	A method of numerical solution of cauchy-type singular integral equations with generalized kernels and arbitrary complex singularities	en
heal.type	journalArticle	en
heal.publicationDate	1979	en
heal.abstract	A numerical method is proposed for the approximate solution of a Cauchy-type singular integral equation (or an uncoupled system of such equations) of the first or the second kind and with a generalized kernel, in the sense that, besides the Cauchy singular part, the kernel has also a Fredholm part presenting strong singularities when both its variables tend to the same end-point of the integration interval. In this case any type of real or generally complex singularities in the unknown function of the integral equation may be present near the end-points of the integration interval. The method proposed consists simply in approximating the integrals in the integral equation by using an appropriate numerical integration rule with generally complex abscissas and weights, followed by the application of the resulting approximate equation at properly selected complex collocation points lying outside the integration interval. Although no proof of the convergence of the method seems possible, this method was seen to exhibit good convergence to the results expected in an example treated. © 1979.	en
heal.journalName	Journal of Computational Physics	en
dc.identifier.volume	30	en
dc.identifier.issue	3	en
dc.identifier.spage	309	en
dc.identifier.epage	323	en