Publication: The swallowtail integral in the highly oscillatory region II
| 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 | 2021-09-06T12:27:35Z | |
| dc.date.available | 2021-09-06T12:27:35Z | |
| dc.date.issued | 2020 | |
| dc.description.abstract | We analyze the asymptotic behavior of the swallowtail integral R ∞ −∞ e i(t 5+xt3+yt2+zt)dt for large values of |y| and bounded values of |x| and |z|. We use the simpli ed saddle point method introduced in [López et al., 2009]. With this method, the analysis is more straightforward than with the standard saddle point method and it is possible to derive complete asymptotic expansions of the integral for large |y| and xed x and z. There are four Stokes lines in the sector (−π, π] that divide the complex y−plane in four sectors in which the swallowtail integral behaves di erently when |y| is large. The asymptotic approximation is the sum of two asymptotic series whose terms are elementary functions of x, y and z. One of them is of Poincaré type and is given in terms of inverse powers of y 1/2 . The other one is given in terms of an asymptotic sequence of the order O(y −n/9 ) when |y| → ∞, and it is multiplied by an exponential factor that behaves di erently in the four mentioned sectors. Some numerical experiments illustrate the accuracy of the approximation. | en |
| dc.description.sponsorship | This research was supported by the Ministerio de Economia y Competitividad (MTM2017-83490-P). The Universidad Publica de Navarra is acknowledged by its financial support. | en |
| dc.format.extent | 13 p. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.1553/etna_vol52s88 | |
| dc.identifier.issn | 1068-9613 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/40433 | |
| dc.language.iso | eng | en |
| dc.publisher | Kent State University | en |
| dc.publisher | Johann Radon Institute (RICAM) | en |
| dc.relation.ispartof | Electronic Transactions on Numerical Analysis, 52, 88-99 | 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/10.1553/etna_vol52s88 | |
| dc.rights | © 2020, Kent State University | 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 II | 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 | |
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