An asymptotic expansion for product integration applied to Cauchy principal value integrals

P. Wesseling

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    Abstract

    Product integration methods for Cauchy principal value integrals based on piecewise Lagrangian interpolation are studied. It is shown that for this class of quadrature methods the truncation error has an asymptotic expansion in integer powers of the step-size, and that a method with an asymptotic expansion in even powers of the step-size does not exist. The relative merits of a quadrature method which employs values of both the integrand and its first derivative and for which the truncation error has an asymptotic expansion in even powers of the step-size are discussed.
    Original languageUndefined
    Pages (from-to)435-442
    JournalNumerische Mathematik
    Volume24
    Issue number5
    DOIs
    Publication statusPublished - 1975

    Keywords

    • IR-85605

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