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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Asymptotic expansions for product integration

Authors: Frank de Hoog and Richard Weiss
Journal: Math. Comp. 27 (1973), 295-306
MSC: Primary 65D30
MathSciNet review: 0329207
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Abstract: A generalized Euler-Maclaurin sum formula is established for product integration based on piecewise Lagrangian interpolation. The integrands considered may have algebraic or logarithmic singularities. The results are used to obtain accurate convergence rates of numerical methods for Fredholm and Volterra integral equations with singular kernels.

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Keywords: Product integration, asymptotic expansion, Euler-Maclaurin sum formula, integral equation
Article copyright: © Copyright 1973 American Mathematical Society