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Numerical evaluation of Airy-type integrals arising in uniform asymptotic analysis

Abstract: We describe a method to evaluate integrals that arise in the asymptotic analysis when two saddle points may be close together. These integrals, which appear in problems from optics, acoustics or quantum mechanics as well as in a wide class of special functions, can be transformed into Airy-type integrals and we use the trapezoidal rule to compute these integrals numerically. The quadrature method, which remains valid when two saddle points coalesce, is illustrated with numerical examples.

 Authorship: Gil A., Segura J., Temme N.,

 Fuente: Journal of Computational and Applied Mathematics Volume 371, June 2020, 112717

 Publisher: Elsevier

 Publication date: 01/06/2020

 No. of pages: 29

 Publication type: Article

 DOI: 10.1016/

 ISSN: 0377-0427,1879-1778

 Spanish project: MTM2015-67142-P ; PGC2018-098279-B-I00

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