On numerical evaluation of integrals involving Bessel functions

Václav Bezvoda; Ruszlán Farzan; Karel Segeth; Galina Takó

Aplikace matematiky (1986)

  • Volume: 31, Issue: 5, page 396-410
  • ISSN: 0862-7940

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Bezvoda, Václav, et al. "On numerical evaluation of integrals involving Bessel functions." Aplikace matematiky 31.5 (1986): 396-410. <http://eudml.org/doc/15463>.

@article{Bezvoda1986,
abstract = {},
author = {Bezvoda, Václav, Farzan, Ruszlán, Segeth, Karel, Takó, Galina},
journal = {Aplikace matematiky},
keywords = {integrals with Bessel functions; fast Fourier transform; Gaussian integration formula; five-point Gauss rule; error analysis; numerical quadrature; integrals with Bessel functions; fast Fourier transform; Gaussian integration formula; five-point Gauss rule; error analysis},
language = {eng},
number = {5},
pages = {396-410},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On numerical evaluation of integrals involving Bessel functions},
url = {http://eudml.org/doc/15463},
volume = {31},
year = {1986},
}

TY - JOUR
AU - Bezvoda, Václav
AU - Farzan, Ruszlán
AU - Segeth, Karel
AU - Takó, Galina
TI - On numerical evaluation of integrals involving Bessel functions
JO - Aplikace matematiky
PY - 1986
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 31
IS - 5
SP - 396
EP - 410
AB -
LA - eng
KW - integrals with Bessel functions; fast Fourier transform; Gaussian integration formula; five-point Gauss rule; error analysis; numerical quadrature; integrals with Bessel functions; fast Fourier transform; Gaussian integration formula; five-point Gauss rule; error analysis
UR - http://eudml.org/doc/15463
ER -

References

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  1. M. Ambrožová, Using fast Fourier transform for evaluation of the integral of an oscillating function on the infinite integral, (Czech.) RNDr. thesis. Matematicko-fyzikální fakulta Univerzity Karlovy, Praha 1979. (1979) 
  2. N. S. Bahvalov, Numerical Methods, (Russian.) Nauka, Moskva 1973. (1973) MR0362811
  3. I. S. Berezin I. P. Židkov, Methods of Computation, (Russian.) Vol. 1. Nauka, Moskva 1966. (1966) 
  4. V. Bezvoda K. Segeth, 10.1007/BF01617648, Studia Geod. et Geoph. 20 (1976), 366-377. (1976) DOI10.1007/BF01617648
  5. V. Bezvoda K. Segeth, Mathematical Modeling in Electromagnetic Prospecting Methods, Univerzita Karlova, Praha 1982. (1982) 
  6. P. I. Davis P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York 1975. (1975) MR0448814
  7. R. H. Farzan, Propagation of electromagnetic waves in stratified media with local inhomogeneity, Mathematical Models in Physics and Chemistry and Numerical Methods of Their Realization. Teubner Texte zur Mathematik 61. Teubner, Leipzig 1984, 237-247. (1984) 
  8. L. N. G. Filon, On a quadrature formula for trigonometric integrals, Proc. Roy. Soc. Edinburgh 49 (1928), 38-47. (1928) 
  9. I. S. Gradštein I. M. Ryžik, Tables of Integrals, Sums, Series, and Products, (Russian.) 5th ed. Nauka, Moskva 1971. (1971) 
  10. S.-Å. Gustafson G. Dahlqaist, On the computation of slowly convergent Fourier integrals, Methoden und Verfahren der mathematischen Physik. Band 6. Bibliographisches Institut, Mannheim 1972, 93-112. (1972) MR0359377
  11. T. Kaneko B. Liu, 10.1145/321607.321613, J. Assoc. Comput. Mach. 17 (1970), 637-654. (1970) MR0275710DOI10.1145/321607.321613
  12. V. I. Krylov, Approximate Computation of Integrals, (Russian.) Nauka, Moskva 1967. (1967) MR0218015
  13. I. M. Longman, 10.1017/S030500410003187X, Proc. Camb. Phil. Soc. 52 (1956), 764-768. (1956) Zbl0072.33803MR0082193DOI10.1017/S030500410003187X
  14. R. Piessens E. de Doncker-Kapenga C. W. Überhuber D. K. Kahaner, QUADPACK. A Subroutine Package for Automatic Integration, Springer Series in Computational Mathematics 1. Springer-Verlag, Berlin 1983. (1983) MR0712135
  15. A. Ralston, A First Course in Numerical Analysis, McGraw-Hill, New York 1965. (1965) Zbl0139.31603MR0191070
  16. K. Segeth, Roundoff errors in the fast computation of discrete convolutions, Apl. Mat. 26 (1981), 241-262. (1981) Zbl0474.65025MR0623505
  17. H. J. Stetter, 10.1007/BF02162560, Numer. Math. 8 (1966), 235-249. (1966) Zbl0163.39503MR0198716DOI10.1007/BF02162560

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