Skip to main content

A Gaussian quadrature rule for oscillatory integrals on a bounded interval

Asheim, Andreas, Deaño, Alfredo, Huybrechs, Daan, Wang, Haiyong (2014) A Gaussian quadrature rule for oscillatory integrals on a bounded interval. Discrete and Continuous Dynamical Systems - A, 34 (3). pp. 883-901. ISSN 1078-0947. (doi:10.3934/dcds.2014.34.883) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.3934/dcds.2014.34.883

Abstract

We investigate a Gaussian quadrature rule and the corresponding orthogonal polynomials for the oscillatory weight function eiωx on the interval [−1,1]. We show that such a rule attains high asymptotic order, in the sense that the quadrature error quickly decreases as a function of the frequency ω. However, accuracy is maintained for all values of ω and in particular the rule elegantly reduces to the classical Gauss-Legendre rule as ω→0. The construction of such rules is briefly discussed, and though not all orthogonal polynomials exist, it is demonstrated numerically that rules with an even number of points are well defined. We show that these rules are optimal both in terms of asymptotic order as well as in terms of polynomial order.

Item Type: Article
DOI/Identification number: 10.3934/dcds.2014.34.883
Uncontrolled keywords: Numerical quadrature, Gaussian quadrature, orthogonal polynomials., highly oscillatory quadrature
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Alfredo Deano-Cabrera
Date Deposited: 20 Nov 2018 17:49 UTC
Last Modified: 05 Jun 2019 14:47 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/70211 (The current URI for this page, for reference purposes)
Deaño, Alfredo: https://orcid.org/0000-0003-1704-247X
  • Depositors only (login required):