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Algorithm 22 Algorithm for the automatic integration of highly oscillatory functions

Algorithmus für das automatische Integrieren von stark oszillierenden Funktionen

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Abstract

An automatic integration routine for the computation of highly oscillating functions is presented. The algorithm is based on the use of Gaussian quadrature formulas with suitable weight function.

Zusammenfassung

Es wird ein FORTRAN-Programm dargestellt zur automatischen Berechnung bestimmter Integrale mit stark oszillierendem Integrand. Die Integration wird durchgeführt mit Hilfe von speziellen Quadraturformeln vom Gaußschen Typ.

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References

  1. Chase, S. M., and L. D. Fosdick: Algorithm 353, Filon quadrature. Comm. ACM12, 475 (1969).

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  2. Einarsson, B.: Algorithm 418, Calculation of Fourier Integrals. Comm. ACM15, 47 (1972).

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  3. Piessens, R.: Gaussian quadrature formulas for the integration of oscillatory functions. ZAMM50, 698 (1970).

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  4. Piessens, R.: Gaussian quadrature formulas for the calculation of Fourier-Cosine coefficients. ZAMM52, 56 (1972).

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  5. Piessens, R.: An algorithm for automatic integration. Angewandte Informatik15, 399 (1973).

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Authors and Affiliations

  1. Applied Mathematics and Programming Division, University of Leuven, Celestijnenlaan 200 B, B-3030, Heverlee, Belgium

    R. Piessens & Ann Haegemans

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  1. R. Piessens
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  2. Ann Haegemans
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Piessens, R., Haegemans, A. Algorithm 22 Algorithm for the automatic integration of highly oscillatory functions. Computing 13, 183–193 (1974). https://doi.org/10.1007/BF02246617

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  • DOI: https://doi.org/10.1007/BF02246617

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