Person:
Pรฉrez Sinusรญa, Ester

Profile Picture

Email Address

person.page.identifierURI

https://academica-e.unavarra.es/handle/2454/49788

Birth Date

Research Projects

Organizational Units

Job Title

Last Name

Pรฉrez Sinusรญa

First Name

Ester

person.page.departamento

Ingenierรญa Matemรกtica e Informรกtica

person.page.instituteName

ORCID

0000-0002-8021-2745

person.page.upna

7326

Name

Filters

20231
Reset filters

Settings

Subject: Catastrophe integrals ร— Subject: Asymptotic expansions ร—

Search Results

Now showing 1 - 1 of 1
  • Thumbnail Image
    PublicationOpen Access
    Asymptotic approximation of a highly oscillatory integral with application to the canonical catastrophe integrals
    (Wiley, 2023) Ferreira Gonzรกlez, Chelo; Lรณpez Garcรญa, Josรฉ Luis; Pรฉrez Sinusรญa, Ester; Estadรญstica, Informรกtica y Matemรกticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Universidad Pรบblica de Navarra / Nafarroako Unibertsitate Publikoa
    We consider the highly oscillatory integral ๐น(๐‘ค) โˆถ= โˆซ โˆž โˆ’โˆž ๐‘’๐‘–๐‘ค(๐‘ก๐พ+2+๐‘’๐‘–๐œƒ๐‘ก๐‘) ๐‘”(๐‘ก)๐‘‘๐‘ก for large positive values of ๐‘ค, โˆ’๐œ‹ < ๐œƒ โ‰ค ๐œ‹, ๐พ and ๐‘ positive integers with 1 โ‰ค ๐‘ โ‰ค ๐พ, and ๐‘”(๐‘ก) an entire function. The standard saddle point method is complicated and we use here a simplified version of this method introduced by Lรณpez et al. We derive an asymptotic approximation of this integral when ๐‘ค โ†’ +โˆž for general values of ๐พ and ๐‘ in terms of elementary functions, and determine the Stokes lines. For ๐‘ โ‰  1, the asymptotic behavior of this integral may be classified in four different regions according to the even/odd character of the couple of parameters ๐พ and ๐‘; the special case ๐‘=1 requires a separate analysis. As an important application, we consider the family of canonical catastrophe integrals ฮจ๐พ(๐‘ฅ1, ๐‘ฅ2,โ€ฆ,๐‘ฅ๐พ) for large values of one of its variables, say ๐‘ฅ๐‘, and bounded values of the remaining ones. This family of integrals may be written in the form ๐น(๐‘ค) for appropriate values of the parameters ๐‘ค, ๐œƒ and the function ๐‘”(๐‘ก). Then, we derive an asymptotic approximation of the family of canonical catastrophe integrals for large |๐‘ฅ๐‘|. The approximations are accompanied by several numerical experiments. The asymptotic formulas presented here fill up a gap in the NIST Handbook of Mathematical Functions by Olver et al.