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Complex Gaussian quadrature of oscillatory integrals

Deaño, Alfredo, Huybrechs, Daan (2009) Complex Gaussian quadrature of oscillatory integrals. Numerische Mathematik, 112 (2). pp. 197-219. ISSN 0029-599X. (doi:10.1007/s00211-008-0209-z) (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/10.1007/s00211-008-0209-z

Abstract

We construct and analyze Gauss-type quadrature rules with complex- valued nodes and weights to approximate oscillatory integrals with stationary points of high order. The method is based on substituting the original interval of integration by a set of contours in the complex plane, corresponding to the paths of steepest descent. Each of these line integrals shows an exponentially decaying behaviour, suitable for the application of Gaussian rules with non-standard weight functions. The results differ from those in previous research in the sense that the constructed rules are asymptotically optimal, i.e., among all known methods for oscillatory integrals they deliver the highest possible asymptotic order of convergence, relative to the required number of evaluations of the integrand.

Item Type: Article
DOI/Identification number: 10.1007/s00211-008-0209-z
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Alfredo Deano-Cabrera
Date Deposited: 21 Nov 2018 10:55 UTC
Last Modified: 30 May 2019 08:21 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/70233 (The current URI for this page, for reference purposes)
Deaño, Alfredo: https://orcid.org/0000-0003-1704-247X
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