On the numerical quadrature of highly-oscillating integrals I: Fourier transforms
نویسنده
چکیده
Highly-oscillatory integrals are allegedly difficult to calculate. The main assertion of this paper is that that impression is incorrect. As long as appropriate quadrature methods are used, their accuracy increases when oscillation becomes faster and suitable choice of quadrature points renders this welcome phenomenon more pronounced. We focus our analysis on Filon-type quadrature and analyse its behaviour in a range of frequency regimes for integrals of the form ∫ h 0 f (x)e iωxw(x)dx , where h > 0 is small and |ω| large. Our analysis is applied to modified Magnus methods for highly-oscillatory ordinary differential equations.
منابع مشابه
Numerical integration of highly–oscillating functions
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....
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