Procedures for computing one- and two-dimensional integrals of functions with rapid irregular oscillations
Math. Comp. 38 (1982), 531-538
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Abstract: A collocation procedure for efficient integration of rapidly oscillatory functions is presented. The integration problem is transformed into a certain O.D.E. problem, and this is solved by a collocation technique. The method is also extended to two-dimensional integration, and some numerical results are appended showing the efficiency of the method in handling difficult cases of rapid irregular oscillations.
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. MR 0448814
de Boor and Blâir
Swartz, Collocation at Gaussian points, SIAM J. Numer. Anal.
10 (1973), 582–606. MR 0373328
L. N. G. Filon, "On a quadrature formula for trigonometric integrals," Proc. Roy. Soc. Edinburgh, v. 49, 1928, pp. 38-47.
A. Flinn, A modification of Filon’s method of numerical
integration, J. Assoc. Comput. Mach. 7 (1960),
181–184. MR 0114298
M. Longman, A method for the numerical evaluation
of finite integrals of oscillatory functions, Math. Comput. 14 (1960), 53–59. MR 0111136
(22 #2000), http://dx.doi.org/10.1090/S0025-5718-1960-0111136-X
- P. J. Davis & P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York, 1975. MR 0448814 (56:7119)
- Carl de Boor & B. Swartz, "Collocation at Gaussian points," SIAM J. Numer. Anal., v. 10, 1973, pp. 582-606. MR 0373328 (51:9528)
- L. N. G. Filon, "On a quadrature formula for trigonometric integrals," Proc. Roy. Soc. Edinburgh, v. 49, 1928, pp. 38-47.
- E. A. Flinn, "A modification of Filon's method of numerical integration," J. Assoc. Comput. Mach., v. 7, 1960, pp. 181-184. MR 0114298 (22:5122)
- I. M. Longman, "A method for the numerical evaluation of finite integrals of oscillatory functions," Math. Comp., v. 14, 1960, pp. 53-59. MR 0111136 (22:2000)
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