Publication:
An asymptotic expansion of the hyberbolic umbilic catastrophe integral

Date

2022

Director

Publisher

Springer
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión publicada / Argitaratu den bertsioa

Project identifier

Abstract

We obtain an asymptotic expansion of the hyperbolic umbilic catastrophe integral Ψ(H) (x,y,z) := ∫∞−∞∫∞−∞exp(i(s3+t3+zst +yt+xs))ds dt for large values of |x| and bounded values of |y| and |z|. The expansion is given in terms of Airy functions and inverse powers of x. There is only one Stokes ray at argx=π . We use the modified saddle point method introduced in (López et al. J Math Anal Appl 354(1):347–359, 2009). The accuracy and the asymptotic character of the approximations are illustrated with numerical experiments.

Description

Keywords

Asymptotic approximations, Hyperbolic umbilic catastrophe integral, Modified saddle point method

Department

Estadística, Informática y Matemáticas / Estatistika, Informatika eta Matematika / Institute for Advanced Materials and Mathematics - INAMAT2

Faculty/School

Degree

Doctorate program

item.page.cita

Ferreira, C., López, J. L., & Pérez Sinusía, E. (2022). An asymptotic expansion of the hyberbolic umbilic catastrophe integral. The Ramanujan Journal. https://doi.org/10.1007/s11139-022-00675-0

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