Corrected trapezoidal rules for a class of singular functions
2014 (English)In: IMA Journal of Numerical Analysis, ISSN 0272-4979, E-ISSN 1464-3642, Vol. 34, no 4, 1509-1540 p.Article in journal (Refereed) Published
A set of accurate quadrature rules applicable to a class of integrable functions with isolated singularities is designed and analysed theoretically in one and two dimensions. These quadrature rules are based on the trapezoidal rule with corrected quadrature weights for points in the vicinity of the singularity. To compute the correction weights, small-size ill-conditioned systems have to be solved. The convergence of the correction weights is accelerated by the use of compactly supported functions that annihilate boundary errors. Convergence proofs with error estimates for the resulting quadrature rules are given in both one and two dimensions. The tabulated weights are specific for the singularities under consideration, but the methodology extends to a large class of functions with integrable isolated singularities. Furthermore, in one dimension we have obtained a closed form expression based on which the modified weights can be computed directly.
Place, publisher, year, edition, pages
2014. Vol. 34, no 4, 1509-1540 p.
singular functions, quadrature methods, high order
IdentifiersURN: urn:nbn:se:kth:diva-29760DOI: 10.1093/imanum/drt046ISI: 000343320900008ScopusID: 2-s2.0-84904197227OAI: oai:DiVA.org:kth-29760DiVA: diva2:397500
QC 20141121. Updated from submitted to published.2011-02-152011-02-152014-11-21Bibliographically approved