zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Analysis of a collocation method for integrating rapidly oscillatory functions. (English) Zbl 0870.65019
The author analyses a collocation method for approximating integrals of rapidly oscillatory functions. The studied method is efficient for integrals involving Bessel functions $J_\nu (rx)$ with a large oscillating frequency parameter $r$, as well as for many other one- and multidimensional integrals of functions with rapid irregular oscillations. The analysis provides a convergence rate and it shows that the relative error of the method is even decreasing as the frequency of the oscillations increases.

MSC:
65D32Quadrature and cubature formulas (numerical methods)
41A55Approximate quadratures
WorldCat.org
Full Text: DOI
References:
[1] Levin, D.: Procedures for computing one- and two-dimensional integrals of functions with rapid irregular oscillations. Math. comp. 38, 531-538 (1982) · Zbl 0482.65013
[2] Levin, D.: Fast integration of rapidly oscillatory functions. J. comput. Appl. math. 63, 95-101 (1995) · Zbl 0858.65017
[3] Levin, D.; Reichel, L.; Ringhofer, C.: Analysis of an integration method for rapidly oscillating integrands. MRC report no. 2670 (1984)