On the quadrature of multivariate highly oscillatory integrals over non-polytope domains

Numerische Mathematik

Volumn 103, Issue 4, 2006, Pages 643-665

  Olver, Sheehan ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33744750511     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-006-0009-2     Document Type: Article

References (11)

1. Cheney, W., Light, W.: A course in approximation theory. Pacific Grove, CA: Brooks/Cole Publishing Company 2000
2. Iserles, A., Nørsett, S.P.: On quadrature methods for highly oscillatory integrals and their implementation. BIT 44, 755-772 (2004)
3. Iserles, A., Nørsett, S.P.: Efficient quadrature of highly oscillatory integrals using derivatives. Proc R Soc A 461, 1383-1399 (2005)
4. Iserles, A., Nørsett, S.P.: On the computation of highly oscillatory multivariate integrals with critical points. Technical Report NA2005/08, DAMTP, University of Cambridge 2005
5. Iserles, A., Nørsett, S.P.: Quadrature methods for multivariate highly oscillatory integrals using derivatives. Technical Report NA2005/02, DAMTP, University of Cambridge, Math Comput (2005) (in press)
6. Levin, D.: Analysis of a collocation method for integrating rapidly oscillatory functions. J Comput Appl Maths 78, 131-138 (1997)
7. Olver, F.W.J.: Asymptotics and special functions. New York, NY: Academic 1974
8. Olver, S.: Moment-free numerical integration of highly oscillatory functions. Technical Report NA2005/04, DAMTP, University of Cambridge, IMA J Num Anal 26, 213-227 (2006)
9. Powell, M.J.D.: Approximation theory and methods. Cambridge: Cambridge University Press 1981
10. Press, W.H., Flannery, B.P., Teukolsky, S., Vetterling, W.T.: Numerical recipes in C: the art of scientific computing. Cambridge: Cambridge Unversity Press 1988
11. Stein, E. : Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. Princeton, NJ: Princeton University Press 1993