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Analysis of a collocation method for integrating rapidly oscillatory functions. (English) Zbl 0870.65019
The author analyses a collocation method for approximating integrals of rapidly oscillatory functions. The studied method is efficient for integrals involving Bessel functions $J_\nu (rx)$ with a large oscillating frequency parameter $r$, as well as for many other one- and multidimensional integrals of functions with rapid irregular oscillations. The analysis provides a convergence rate and it shows that the relative error of the method is even decreasing as the frequency of the oscillations increases.

65D32Quadrature and cubature formulas (numerical methods)
41A55Approximate quadratures
Full Text: DOI
[1] Levin, D.: Procedures for computing one- and two-dimensional integrals of functions with rapid irregular oscillations. Math. comp. 38, 531-538 (1982) · Zbl 0482.65013
[2] Levin, D.: Fast integration of rapidly oscillatory functions. J. comput. Appl. math. 63, 95-101 (1995) · Zbl 0858.65017
[3] Levin, D.; Reichel, L.; Ringhofer, C.: Analysis of an integration method for rapidly oscillating integrands. MRC report no. 2670 (1984)