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Procedures for computing one- and two-dimensional integrals of functions with rapid irregular oscillations. (English) Zbl 0482.65013

MSC:
65D32 Numerical quadrature and cubature formulas
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
65R10 Numerical methods for integral transforms
41A55 Approximate quadratures
41A63 Multidimensional problems
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References:
[1] Philip J. Davis and Philip Rabinowitz, Methods of numerical integration, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers] New York-London, 1975. Computer Science and Applied Mathematics. · Zbl 0304.65016
[2] Carl de Boor and Blâir Swartz, Collocation at Gaussian points, SIAM J. Numer. Anal. 10 (1973), 582 – 606. · Zbl 0232.65065
[3] L. N. G. Filon, ”On a quadrature formula for trigonometric integrals,” Proc. Roy. Soc. Edinburgh, v. 49, 1928, pp. 38-47. · JFM 55.0946.02
[4] E. A. Flinn, A modification of Filon’s method of numerical integration, J. Assoc. Comput. Mach. 7 (1960), 181 – 184. · Zbl 0121.11703
[5] I. M. Longman, A method for the numerical evaluation of finite integrals of oscillatory functions, Math. Comput. 14 (1960), 53 – 59. · Zbl 0097.12105
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