A direct method to quadrature rules for a certain class of singular integrals with logarithmic, Cauchy, or Hadamard-type singularities

Tsalamengas, JL

dc.contributor.author	Tsalamengas, JL	en
dc.date.accessioned	2014-03-01T02:07:17Z
dc.date.available	2014-03-01T02:07:17Z
dc.date.issued	2012	en
dc.identifier.issn	08943370	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29535
dc.subject	integral equations	en
dc.subject	Nyström method	en
dc.subject	quadrature rules	en
dc.subject	singular integrals	en
dc.subject.other	Conducting strips	en
dc.subject.other	Direct method	en
dc.subject.other	Hadamard-type singularity	en
dc.subject.other	Integral equation formulation	en
dc.subject.other	Loss of accuracy	en
dc.subject.other	M method	en
dc.subject.other	Numerical example	en
dc.subject.other	Numerical quadrature	en
dc.subject.other	Potential problems	en
dc.subject.other	Quadrature rules	en
dc.subject.other	Singular integral	en
dc.subject.other	Wave diffractions	en
dc.subject.other	Integral equations	en
dc.subject.other	Numerical methods	en
dc.title	A direct method to quadrature rules for a certain class of singular integrals with logarithmic, Cauchy, or Hadamard-type singularities	en
heal.type	journalArticle	en
heal.identifier.primary	10.1002/jnm.1863	en
heal.identifier.secondary	http://dx.doi.org/10.1002/jnm.1863	en
heal.publicationDate	2012	en
heal.abstract	Singular integrals of the form ∫-11 w(τ)f(τ)K(t,τ)dτ with logarithmic, Cauchy, or Hadamard-type singularities in addition to endpoint algebraic singularities w(τ) = (1 - τ2)± 1/2 are frequently encountered in integral equation formulations of potential problems. Some of the existing quadratures for the evaluation of such integrals only apply to preassigned values of the external variable t. Other fairly general rules suffer from loss of accuracy when t is close to any of the nodes of the quadrature. Finally, derivation of the rules is in general multistage, and thus, considerable analytical preprocessing is required. In this paper, a straightforward direct method is presented, which demonstrates the derivation of numerical quadrature rules for Cauchy-type and Hadamard-type integrals from corresponding quadratures pertinent to logarithmically singular integrals. The proposed rules share the following characteristics: (1) their derivation, based on first principles, is remarkably simple; (2) the external variable t may be arbitrarily selected; and (3) in their framework, the loss of accuracy referred to earlier is fully remedied. Numerical examples and case studies illustrate the simplicity, flexibility, and high accuracy of the algorithms. Application to the solution of an integral equation associated with wave diffraction by a perfectly conducting strip is exemplified. Copyright © 2012 John Wiley & Sons, Ltd.	en
heal.journalName	International Journal of Numerical Modelling: Electronic Networks, Devices and Fields	en
dc.identifier.doi	10.1002/jnm.1863	en
dc.identifier.volume	25	en
dc.identifier.issue	5-6	en
dc.identifier.spage	512	en
dc.identifier.epage	524	en