A user-friendly extrapolation method for computing infinite range integrals of products of oscillatory functions

IMA Journal of Numerical Analysis

Volumn 32, Issue 2, 2012, Pages 602-631

  Sidi, Avram ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Asymptotic expansions; Bessel functions; Extrapolation methods; Infinite range oscillatory integrals; MW transformation; Numerical integration; W algorithm

Indexed keywords

ASYMPTOTIC ANALYSIS; BESSEL FUNCTIONS; EXTRAPOLATION;

ASYMPTOTIC EXPANSION; EXTRAPOLATION METHODS; MW-TRANSFORMATION; NUMERICAL INTEGRATIONS; OSCILLATORY INTEGRAL;

NUMERICAL METHODS;

EID: 84863208134     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drr022     Document Type: Article

References (15)

1. BAILEY, D. H. & BORWEIN, J. M. (2011) Hand-to-hand combat with thousand-digit integrals. J. Comput. Sci. (in press).
2. LEVIN, D. & SIDI, A. (1981) Two new classes of nonlinear transformations for accelerating the convergence of infinite integrals and series. Appl. Math. Comput., 9, 175-215. Originally appeared as a Tel Aviv University preprint in 1975.
3. LUCAS, S. K. (1995) Evaluating infinite integrals involving products of Bessel functions of arbitrary order. J. Comput. Appl. Math., 64, 269-282.
4. OLVER, F. W. J., LOZIER, D. W., BOISVERT, R. F. & CLARK, C. W. (eds) (2010) NIST Handbook of Mathematical Functions. Cambridge: Cambridge University Press.
5. SIDI, A. (1979) Some properties of a generalization of the Richardson extrapolation process. J. Inst. Maths. Applics., 24, 327-346.
6. SIDI, A. (1980) Extrapolation methods for oscillatory infinite integrals. J. Inst. Maths. Applics., 26, 1-20.
7. SIDI, A. (1982a) An algorithm for a special case of a generalization of the Richardson extrapolation process. Numer. Math., 38, 299-307.
8. SIDI, A. (1982b) The numerical evaluation of very oscillatory infinite integrals by extrapolation. Math. Comput., 38, 517-529.
9. SIDI, A. (1987) Extrapolation methods for divergent oscillatory infinite integrals that are defined in the sense of summability. J. Comput. Appl. Math., 17, 105-114. (Pubitemid 17534228)
10. SIDI, A. (1988) A user-friendly extrapolation method for oscillatory infinite integrals. Math. Comput., 51, 249-266.
11. SIDI, A. (1997) Computation of infinite integrals involving Bessel functions of arbitrary order by the D̄ -transformation. J. Comput. Appl. Math., 78, 125-130. (Pubitemid 127417802)
12. SIDI, A. (1999) Further convergence and stability results for the generalized Richardson extrapolation process GREP(1) with an application to the D(1)-transformation for infinite integrals. J. Comput. Appl. Math., 112, 269-290. (Pubitemid 30512750)
13. SIDI, A. (2003) Practical Extrapolation Methods: Theory and Applications. Number 10 in Cambridge Monographs on Applied and Computational Mathematics. Cambridge: Cambridge University Press.
14. VAN DEUN, J. & COOLS, R. (2006) Computing infinite range integrals of an arbitrary product of Bessel functions. ACM Trans. Math. Softw., 32, 580-596. (Pubitemid 44927145)
15. VAN DEUN, J. & COOLS, R. (2008) Integrating products of Bessel functions with an additional exponential or rational factor. Comput. Phys. Commun., 178, 578-590.