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Newton-Cotes Formulae for the Numerical Evaluation of Certain Hypersingular Integrals

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Abstract

The quadrature formulae of Newton-Cotes type for the computation of hypersingular integrals with second order singularity on interval are discussed. We improve the estimates given by Linz [22] such that the Newton-Cotes method is valid with less restriction on the location of the singular point. We also present a new Newton-Cotes formula which is applicable when the singular point coincides with a mesh point, while the classical Newton-Cotes method fails in this case. Error analysis for the new formula is given. Numerical experiments are presented to validate the analysis.

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Authors and Affiliations

  1. Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, P. R. China

    Weiwei Sun

  2. Laboratory of Computational Physics, Inst. of Applied Physics and Computational Mathematics, P. O. Box 8009, Bei**g, 100088, P. R. China

    Jiming Wu

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  1. Weiwei Sun
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  2. Jiming Wu
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Sun, W., Wu, J. Newton-Cotes Formulae for the Numerical Evaluation of Certain Hypersingular Integrals. Computing 75, 297–309 (2005). https://doi.org/10.1007/s00607-005-0131-5

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