DOI
10.34229/KCA2522-9664.24.2.11
UDC 519.6
OPTIMAL CALCULATION OF INTEGRALS OF RAPIDLY OSCILLATING
FUNCTIONS FOR SOME CLASSES OF DIFFERENTIAL FUNCTIONS
Abstract. The author considers the problem of calculating integrals of rapidly oscillating functions from some classes of differential functions, in particular, in the case of the interpolation class of functions, where the information operator is specified by a fixed table of its values. Quadrature formulas for calculating integrals of rapidly oscillating functions have been constructed that are optimal in terms of accuracy and optimal in order of accuracy. The optimal estimates for the error of the method are obtained.
Keywords: integrals of rapidly oscillating functions, interpolation classes of functions, quadrature formulas optimal in terms of accuracy, method of boundary functions, lower estimate of numerical integration error.
full text
REFERENCES
- Drachman B., Ross J. Approximation of certain functions given by integrals with highly oscillatory integrands. IEEE Trans. Antennas Propagation. 1994. Vol. 42, N 9. P. 1355–1356.
- Gold B., Rader C.M. Digital Processing of Signals. Krieger, 1983. 269 p.
- Leondes C.T. (Ed.) Digital control and signal processing systems and techniques. San-Diego, CA.: Academic Press, 1996. 398 p.
- Haider Q., Liu L.C. Fourier and Bessel transformations of highly oscillatory functions. J. Phys. 1992. A 25. P. 6755–6760.
- Filon L.N. On a quadrature formula for trigonometric integrals. Proc. Roy. Soc. Edinburg. 1928. Vol. 49. P. 38–47.
- Flinn E.A. A modification of Filon’s method of numerical integration. J. Assoc. Comput. Mach. 1960. N 7. P. 181–184.
- Luke Y.L. On the computation of oscillatory integrals. Part 2. Proc. Cambridge Philos. Soc. 1964. Vol. 50. P. 269–277.
- Zadiraka V.K., Melnikova S.S., Luts L.V. Optimal integration of rapidly oscillating functions in the class W2,L,N with the use of different information operators. Cybernetics and Systems Analysis. 2013. Vol. 49, N 2. P. 229–238. https://doi.org/10.1007/s10559-013-9504-5.
- Zadiraka V.K., Luts L.V., Shvidchenko I.V. Theory of calculations of integrals from fast oscillating functions [in Ukrainian]. Kyiv: Nauk. dumka, 2023. 472 p. https://doi.org/10.15407/978-966-00-1843-3.
- Zavyalov Yu.S., Kvasov B.I., Miroshnichenko V.L. Spline function methods [in Russian]. Moscow: Nauka, 1980. 352 p.
