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

P. Wesseling

    Research output: Contribution to journalArticleAcademic

    2 Citations (Scopus)
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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

    Cite this

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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.",
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    author = "P. Wesseling",
    year = "1975",
    doi = "10.1007/BF01437410",
    language = "Undefined",
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    pages = "435--442",
    journal = "Numerische Mathematik",
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    An asymptotic expansion for product integration applied to Cauchy principal value integrals. / Wesseling, P.

    In: Numerische Mathematik, Vol. 24, No. 5, 1975, p. 435-442.

    Research output: Contribution to journalArticleAcademic

    TY - JOUR

    T1 - An asymptotic expansion for product integration applied to Cauchy principal value integrals

    AU - Wesseling, P.

    PY - 1975

    Y1 - 1975

    N2 - 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.

    AB - 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.

    KW - IR-85605

    U2 - 10.1007/BF01437410

    DO - 10.1007/BF01437410

    M3 - Article

    VL - 24

    SP - 435

    EP - 442

    JO - Numerische Mathematik

    JF - Numerische Mathematik

    SN - 0029-599X

    IS - 5

    ER -