Numerical integration of highly–oscillating functions
نویسندگان
چکیده
By a highly–oscillating function we mean one with large number of local maxima and minima over some interval. The computation of integrals of highly–oscillating functions is one of the most important issues in numerical analysis since such integrals abound in applications in many branches of mathematics as well as in other sciences, e.g., quantum physics, fluid mechanics, electromagnetics, etc. The principal examples of highly–oscillating integrands occur in various transforms, e.g., Fourier transform, Fourier–Bessel transform, etc. The standard methods of numerical integration often require too much computation work and cannot be successfully applied. Because of that, for integrals of highly–oscillating functions there are a large number of special approaches, which are effective. In this paper we give survey of some special quadrature methods for different types of highly-oscillating integrands. The earliest formulas for numerical integration of highly–oscillating functions were given by Filon [12] in 1928. Filon’s approach for the Fourier integral on the finite interval,
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