The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval

Jiming Wu; Weiwei Sun

doi:10.1007/s00211-007-0125-7

Author(s)

Jiming Wu
Weiwei Sun

Related Research Unit(s)

Department of Mathematics

Detail(s)

Original language	English
Pages (from-to)	143-165
Journal / Publication	Numerische Mathematik
Volume	109
Issue number	1
Publication status	Published - Mar 2008

Link(s)

DOI	DOI https://doi.org/10.1007/s00211-007-0125-7 Final Published version
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Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-43049179400&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(a2449f36-4166-4eba-bb05-a8ae19a83ce5).html

Abstract

We study the general (composite) Newton-Cotes rules for the computation of Hadamard finite-part integral with the second-order singularity and focus on their pointwise superconvergence phenomenon, i.e., when the singular point coincides with some a priori known point, the convergence rate is higher than what is globally possible. We show that the superconvergence rate of the (composite) Newton-Cotes rules occurs at the zeros of a special function and prove the existence of the superconvergence points. Several numerical examples are provided to validate the theoretical analysis. © 2007 Springer-Verlag.

Citation Format(s)

[ RIS ] [ BibTeX ]

The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval. / Wu, Jiming; Sun, Weiwei.

In: Numerische Mathematik, Vol. 109, No. 1, 03.2008, p. 143-165.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review

Wu, J & Sun, W 2008, 'The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval', Numerische Mathematik, vol. 109, no. 1, pp. 143-165. https://doi.org/10.1007/s00211-007-0125-7

Wu, J., & Sun, W. (2008). The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval. Numerische Mathematik, 109(1), 143-165. https://doi.org/10.1007/s00211-007-0125-7

Wu J, Sun W. The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval. Numerische Mathematik. 2008 Mar;109(1):143-165. doi: 10.1007/s00211-007-0125-7

Wu, Jiming ; Sun, Weiwei. / The superconvergence of Newton-Cotes rules for the Hadamard finite-part integral on an interval. In: Numerische Mathematik. 2008 ; Vol. 109, No. 1. pp. 143-165.