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Mathematics of Computation

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Error bounds for compound quadrature of weakly singular integrals


Authors: Alan Feldstein and Richard K. Miller
Journal: Math. Comp. 25 (1971), 505-520
MSC: Primary 65D30
MathSciNet review: 0297127
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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.


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DOI: https://doi.org/10.1090/S0025-5718-1971-0297127-4
Keywords: Quadrature, singular integrals, ignoring the singularity, avoiding the singularity, error bounds, convolution integrals, weakly singular, order of convergence
Article copyright: © Copyright 1971 American Mathematical Society