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.
- 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. MR 0448814
- Carl de Boor and Blâir Swartz, Collocation at Gaussian points, SIAM J. Numer. Anal. 10 (1973), 582–606. MR 373328, DOI https://doi.org/10.1137/0710052 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. 7 (1960), 181–184. MR 114298, DOI https://doi.org/10.1145/321021.321029
- I. M. Longman, A method for the numerical evaluation of finite integrals of oscillatory functions, Math. Comput. 14 (1960), 53–59. MR 0111136, DOI https://doi.org/10.1090/S0025-5718-1960-0111136-X
P. J. Davis & P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York, 1975.
Carl de Boor & B. Swartz, "Collocation at Gaussian points," SIAM J. Numer. Anal., v. 10, 1973, pp. 582-606.
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.
I. M. Longman, "A method for the numerical evaluation of finite integrals of oscillatory functions," Math. Comp., v. 14, 1960, pp. 53-59.
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