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On ignoring the singularity in numerical quadrature

Author: R. K. Miller
Journal: Math. Comp. 25 (1971), 521-532
MSC: Primary 65D30
MathSciNet review: 0301901
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Abstract: This paper studies the convergence of numerical quadratures of singular integrands. The singularities are ignored in the sense that whenever a singularity occurs the integrand is redefined to be zero. Several convergence theorems are proved under the assumption that the integrand can be dominated near each singularity by a monotone, integrable function.

References [Enhancements On Off] (What's this?)

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  • [2] P. Rabinowitz, ``Gaussian integration in the presence of a singularity,'' SIAM J. Numer. Anal., v. 4, 1967, pp. 191-201. MR 35 #3881. MR 0213016 (35:3881)
  • [3] W. Gautschi, ``Numerical quadrature in the presence of a singularity,'' SIAM J. Numer. Anal., v. 4, 1967, pp. 357-362. MR 36 #1103. MR 0218014 (36:1103)
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Keywords: Quadrature, singular quadrature, singular integrals, ignoring the singularity, error bounds, weak singularity
Article copyright: © Copyright 1971 American Mathematical Society

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