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Remark on numerical integration

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Summary

Gaussian quadrature is inappropriate for evaluating a definite integral with logarithmic end-point singularities that occurs in the preceding paper [1]. Some modern ways to evaluate the integral are indicated.

Zusammenfassung

Die Gauss'sche Quadraturformel ist nicht das geeignete Mittel zur Auswertung eines in der vorstehenden Arbeit [1] vorkommenden Integrals, dessen Integrand in den Endpunkten logarithmische Singularitäten hat. Wir berechnen das Integral mit Hilfe von drei zeitgemäßen Quadratur-Algorithmen.

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References

  1. E. G. Anastasseou and N. I. Ioakimides,Application of the Cauchy theorem to the location of zeros of sectionally analytic functions. Z. angew. Math. Physik35, 705–711 (1984).

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  3. W. Gander,A simple adaptive quadrature algorithm. Research report 83-03, Seminar für angewandte Mathematik, ETH Zürich.

  4. Y. Katznelson,An introduction to harmonic analysis. Wiley, New York 1968.

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  5. H. Takahashi and M. Mori,Quadrature formulas obtained by variable transformation. Numer. Math.21, 206–219 (1973.

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Authors and Affiliations

  1. Seminar für angewandte Mathematik, Swiss Federal Institute of Technology, Zürich

    P. Henrici

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  1. P. Henrici
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Henrici, P. Remark on numerical integration. Z. angew. Math. Phys. 35, 712–714 (1984). https://doi.org/10.1007/BF00952116

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  • DOI: https://doi.org/10.1007/BF00952116

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