Modified clenshaw-curtis method for the computation of Bessel function integrals

作者: Robert Piessens , Maria Branders

DOI: 10.1007/BF01934465

关键词:

摘要: The numerical evaluation of Bessel function integrals may be difficult when the is rapidly oscillating in interval integration. In method presented here, smooth factor integrand replaced by a truncated Chebyshev series approximation and resulting integral computed exactly. aspects this exact integration are discussed.

参考文章(25)
C. W. Clenshaw, A. R. Curtis, A method for numerical integration on an automatic computer Numerische Mathematik. ,vol. 2, pp. 197- 205 ,(1960) , 10.1007/BF01386223
Peter Linz, A method for computing Bessel function integrals Mathematics of Computation. ,vol. 26, pp. 509- 513 ,(1972) , 10.1090/S0025-5718-1972-0303687-8
A. Erdelyi, Asymptotic Representations of Fourier Integrals and the Method of Stationary Phase Journal of The Society for Industrial and Applied Mathematics. ,vol. 3, pp. 17- 27 ,(1955) , 10.1137/0103002
Walter Gautschi, Computational Aspects of Three-Term Recurrence Relations Siam Review. ,vol. 9, pp. 24- 82 ,(1967) , 10.1137/1009002
R. Piessens, Maria Branders, Approximation for Bessel functions and their application in the computation of Hankel transforms Computers & Mathematics with Applications. ,vol. 8, pp. 305- 311 ,(1982) , 10.1016/0898-1221(82)90012-8
Walter L. Anderson, Fast Hankel Transforms Using Related and Lagged Convolutions ACM Transactions on Mathematical Software. ,vol. 8, pp. 344- 368 ,(1982) , 10.1145/356012.356014
J. Oliver, The numerical solution of linear recurrence relations Numerische Mathematik. ,vol. 11, pp. 349- 360 ,(1968) , 10.1007/BF02166688
W. Gautschi, Algorithm 236: Bessel Functions of the First Kind Communications of the ACM. ,vol. 7, pp. 479- 480 ,(1964) , 10.1145/355586.355587
C. W. Clenshaw, Yudell L. Luke, The Special Functions and Their Approximations Mathematics of Computation. ,vol. 26, pp. 297- ,(1972) , 10.2307/2004747