Procedures for computing one- and two-dimensional integrals of functions with rapid irregular oscillations
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.
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- 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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