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)
Computation of integrals with oscillatory and singular integrands using Chebyshev expansions. (English) Zbl 1255.65073
Summary: We present a general method for computing oscillatory integrals of the form $\int_{-1}^1f(x)G(x)e^{i{\omega }x}dx$, where $f$ is sufficiently smooth on $[-1,1]$, $\omega $ is a positive parameter and $G$ is a product of singular factors of algebraic or logarithmic type. Based on a Chebyshev expansion of $f$ and the properties of Chebyshev polynomials, the proposed method for such integrals is constructed with the help of the expansion of the oscillatory factor $e^{i{\omega }x}$. Furthermore, due to numerically stable recurrence relations for the modified moments, the devised scheme can be employed to compute oscillatory integrals with algebraic or logarithmic singularities at the end or interior points of the interval of integration. Numerical examples are provided to confirm our analysis.

MSC:
65D32Quadrature and cubature formulas (numerical methods)
65D30Numerical integration
WorldCat.org
Full Text: DOI