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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Wesseling, P. An asymptotic expansion for product integration applied to Cauchy principal value integrals. Numer. Math. 24, 435–442 (1975). https://doi.org/10.1007/BF01437410
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DOI: https://doi.org/10.1007/BF01437410