Efficient quadrature for highly oscillatory integrals involving critical points

Journal of Computational and Applied Mathematics

Volumn 206, Issue 2, 2007, Pages 688-698

  Xiang, Shuhuang ^a  

^a CENTRAL SOUTH UNIVERSITY   (China)

Author keywords

Critical point; Effectiveness; Highly oscillatory integral; Quadrature

Indexed keywords

MATHEMATICAL TRANSFORMATIONS;

GAUSS-LEGENDRE QUADRATURE; LEVIN COLLOCATION METHOD; LEVIN-TYPE METHOD; OSCILLATORY FUNCTIONS;

INTEGRAL EQUATIONS;

EID: 34249826934     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.08.018     Document Type: Article

References (12)

1. Davis P.I., and Rabinowitz P. Methods of Numerical Integral Integration. second ed. (1984), Academic Press, New York
2. Evans G.A., and Webster J.R. A high order, progressive method for the evaluation of irregular oscillatory integrals. Appl. Numer. Math. 23 (1997) 205-218
3. Evans G.A., and Webster J.R. A comparison of some methods for the evaluation of highly oscillatory integrals. J. Comput. Appl. Math. 112 (1999) 55-69
4. Filon L.N.G. On a quadrature formula for trigonometric integrals. Proc. Roy. Soc. Edinburgh 49 (1928) 38-47
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. Comp. 38 (1982) 531-538
9. Olver S. Moment-free numerical integration of highly oscillatory functions. IMA. J. Numer. Anal. 26 (2006) 213-227
10. E. Stein, Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ, pp. 235-249.
11. Stroyan K.D. Mathematical Background: Foundations of Infinitesimal Calculus (1997), Academic Press, Inc., New York
12. i ω g (x) d x, J. Comput. Appl. Math., to appear.