On the Filon and Levin methods for highly oscillatory integral ∫ab f (x) ei ω g (x) d x

Journal of Computational and Applied Mathematics

Volumn 208, Issue 2, 2007, Pages 434-439

  Xiang, Shuhuang ^a  

^a CENTRAL SOUTH UNIVERSITY   (China)

Author keywords

Filon method; Levin method; Oscillatory integral

Indexed keywords

INTERPOLATION; LINEAR EQUATIONS; POLYNOMIALS;

FILON METHOD; LEVIN METHOD; OSCILLATORY INTEGRAL;

FUNCTIONS;

EID: 34547655729     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.10.006     Document Type: Article

References (15)

1. Courant R., and Robbins H. What Is Mathematics? An Elementary Approach to Ideas and Methods. second ed. (1996), Oxford University Press, Oxford
2. Filon L.N.G. On a quadrature formula for trigonometric integrals. Proc. Roy. Soc. Edinburgh 49 (1928) 38-47
3. Iserles A. On the numerical quadrature of highly-oscillating integrals I: Fourier transforms. IMA J. Numer. Anal. 24 (2004) 365-391
4. Iserles A. On the numerical quadrature of highly-oscillating integrals II: irregular oscillators. IMA J. Numer. Anal. 25 (2005) 25-44
5. Iserles A., and Nørsett S.P. On quadrature methods for highly oscillatory integrals and their implementation. BIT 44 (2004) 755-772
6. Iserles A., and Nørsett S.P. Efficient quadrature of highly-oscillatory integrals using derivatives. Proc. Roy. Soc. A 461 (2005) 1383-1399
7. Kress R. Numerical Analysis (1998), Springer, New York
8. Levin D. Procedures for computing one-and-two dimensional integrals of functions with rapid irregular oscillations. Math. Comput. 38 (1982) 531-538
9. Levin D. Fast integration of rapidly oscillatory functions. J. Comput. Appl. Math. 67 (1996) 95-101
10. Levin D. Analysis of a collocation method for integrating rapidly oscillatory functions. J. Comput. Appl. Math. 78 (1997) 131-138
11. Longman I.M. A method for numerical evaluation of finite integrals of oscillatory functions. Math. Comput. 14 (1960) 53-59
12. J.F. Price, Discussions of quadrature formulas for use on digital computers, Report D1-82-0052, Boeing Scientific Research Laboratories, 1960.
13. Stein E. Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals (1993), Princeton University Press, Princeton, NJ
14. Stetter H.J. Numerical approximation of Fourier-transforms. Numer. Math. 8 (1966) 235-249
15. Stroyan K.D. Mathematical Background: Foundations of Infinitesimal Calculus (1997), Academic Press, NewYork