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Numerical Integration of Highly Oscillating Functions

In: Analytic Number Theory, Approximation Theory, and Special Functions

Author

Listed:
  • Gradimir V. Milovanović

    (Mathematical Institute of the Serbian Academy of Sciences and Arts)

  • Marija P. Stanić

    (University of Kragujevac, Department of Mathematics and Informatics, Faculty of Science)

Abstract

Some specific nonstandard methods for numerical integration of highly oscillating functions, mainly based on some contour integration methods and applications of some kinds of Gaussian quadratures, including complex oscillatory weights, are presented in this survey. In particular, Filon-type quadratures for weighted Fourier integrals, exponential-fitting quadrature rules, Gaussian-type quadratures with respect to some complex oscillatory weights, methods for irregular oscillators, as well as two methods for integrals involving highly oscillating Bessel functions are considered. Some numerical examples are included.

Suggested Citation

  • Gradimir V. Milovanović & Marija P. Stanić, 2014. "Numerical Integration of Highly Oscillating Functions," Springer Books, in: Gradimir V. Milovanović & Michael Th. Rassias (ed.), Analytic Number Theory, Approximation Theory, and Special Functions, edition 127, pages 613-649, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-0258-3_23
    DOI: 10.1007/978-1-4939-0258-3_23
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