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A modified sinc quadrature rule for functions with poles near the arc of integration

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Abstract

Sinc function approach is used to obtain a quadrature rule for estimating integrals of functions with poles near the are of integration. Special treatment is given to integration over the intervals (−∞, ∞), (0, ∞), and (−1, 1). It is shown that the error of the quadrature rule converges to zero at the rateO(exp(−c√N)) asN → ∞, whereN is the number of nodes used, and wherec is a positive constant which is independent ofN.

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Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, 40506, Lexington, KY, USA

    Bernard Bialecki

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  1. Bernard Bialecki
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Bialecki, B. A modified sinc quadrature rule for functions with poles near the arc of integration. BIT 29, 464–476 (1989). https://doi.org/10.1007/BF02219232

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  • DOI: https://doi.org/10.1007/BF02219232

1980 Math. Subj. Classification (1985)

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