The swallowtail integral in the highly oscillatory region III
| dc.contributor.author | Ferreira González, Chelo | |
| dc.contributor.author | López García, José Luis | |
| dc.contributor.author | Pérez Sinusía, Ester | |
| dc.contributor.department | Estatistika, Informatika eta Matematika | eu |
| dc.contributor.department | Institute for Advanced Materials and Mathematics - INAMAT2 | en |
| dc.contributor.department | Estadística, Informática y Matemáticas | es_ES |
| dc.contributor.funder | Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa | es |
| dc.date.accessioned | 2021-09-06T12:27:36Z | |
| dc.date.available | 2022-01-20T00:00:12Z | |
| dc.date.issued | 2021 | |
| dc.description.abstract | We consider the swallowtail integral Ψ(x,y,z):=∫∞−∞ei(t5+xt3+yt2+zt)dt for large values of |z| and bounded values of |x| and |y|. The integrand of the swallowtail integral oscillates wildly in this region and the asymptotic analysis is subtle. The standard saddle point method is complicated and then we use the modified saddle point method introduced in López et al., A systematization of the saddle point method application to the Airy and Hankel functions. J Math Anal Appl. 2009;354:347–359. The analysis is more straightforward with this method and it is possible to derive complete asymptotic expansions of Ψ(x,y,z) for large |z| and fixed x and y. The asymptotic analysis requires the study of three different regions for argz separated by three Stokes lines in the sector −π<argz≤π. The asymptotic approximation is a certain combination of two asymptotic series whose terms are elementary functions of x, y and z. They are given in terms of an asymptotic sequence of the order O(z−n/12) when |z|→∞, and it is multiplied by an exponential factor that behaves differently in the three mentioned sectors. The accuracy and the asymptotic character of the approximations are illustrated with some numerical experiments. | en |
| dc.description.sponsorship | This research was supported by the Ministerio de Economía y Competitividad (MTM2017-83490-P) and the Universidad Pública de Navarra. | en |
| dc.embargo.lift | 2022-01-20 | |
| dc.embargo.terms | 2022-01-20 | |
| dc.format.extent | 12 p. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.1080/17476933.2020.1868447 | |
| dc.identifier.issn | 1747-6933 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/40436 | |
| dc.language.iso | eng | en |
| dc.publisher | Taylor & Francis | en |
| dc.relation.ispartof | Complex Variables and Elliptic Equations | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83490-P/ES/ | en |
| dc.relation.publisherversion | https://doi.org/10.1080/17476933.2020.1868447 | |
| dc.rights | © 2021 Informa UK Limited, trading as Taylor & Francis Group | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.subject | Swallowtail integral | en |
| dc.subject | Asymptotic expansions | en |
| dc.subject | Modified saddle point method | en |
| dc.title | The swallowtail integral in the highly oscillatory region III | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | en |
| dc.type.version | Versión aceptada / Onetsi den bertsioa | es |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 8b28fd50-66f4-431e-a219-43d8c02bb077 | |
| relation.isAuthorOfPublication | e6cd33c5-6d5e-455c-b8da-32a9702e16c8 | |
| relation.isAuthorOfPublication | 93f891c7-529d-4972-8759-9d943c60949c | |
| relation.isAuthorOfPublication.latestForDiscovery | 8b28fd50-66f4-431e-a219-43d8c02bb077 |