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)
(KAR id:70211)

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. | |

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: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |

Depositing User: | Alfredo Deano Cabrera |

Date Deposited: | 20 Nov 2018 17:49 UTC |

Last Modified: | 17 Aug 2022 11:02 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 |

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