Numerical Integration of Highly Oscillating Functions

Gradimir V. Milovanović () and Marija P. Stanić ()
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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

A chapter in Analytic Number Theory, Approximation Theory, and Special Functions, 2014, pp 613-649 from Springer

Abstract: 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.

Keywords: Orthogonal Polynomial; Quadrature Rule; Algebraic Polynomial; Irregular Oscillator; Hankel Determinant (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-0258-3_23

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DOI: 10.1007/978-1-4939-0258-3_23

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