The Pearcey integral in the highly oscillatory region

We consider the Pearcey integral P(x, y) for large values of |y| and bounded values of |x|. The integrand of the Pearcey integral oscillates wildly in this region and the asymptotic saddle point analysis is complicated. Then we consider here the modified saddle point method introduced in [Lopez, Pér...

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Autores: López García, José Luis, Pagola Martínez, Pedro Jesús
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2016
País:España
Institución:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/31771
Acceso en línea:https://hdl.handle.net/2454/31771
Access Level:acceso abierto
Palabra clave:Pearcey integral
Asymptotic expansions
Modified saddle point method
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spelling The Pearcey integral in the highly oscillatory regionLópez García, José LuisPagola Martínez, Pedro JesúsPearcey integralAsymptotic expansionsModified saddle point methodWe consider the Pearcey integral P(x, y) for large values of |y| and bounded values of |x|. The integrand of the Pearcey integral oscillates wildly in this region and the asymptotic saddle point analysis is complicated. Then we consider here the modified saddle point method introduced in [Lopez, Pérez and Pagola, 2009] [4]. With this method, the analysis is simpler and it is possible to derive a complete asymptotic expansion of P(x, y) for large |y|. The asymptotic analysis requires the study of three different regions for separately. In the three regions, the expansion is given in terms of inverse powers of y2/3 and the coefficients are elementary functions of x. The accuracy of the approximation is illustrated with some numerical experiments.The Universidad Pública de Navarra is acknowledged by its financial support.ElsevierMatematika eta Informatika IngeniaritzaInstitute for Advanced Materials and Mathematics - INAMAT2Ingeniería Matemática e InformáticaUniversidad Pública de Navarra / Nafarroako Unibertsitate Publikoa2016info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2454/31771reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglés© 2015 Elsevier Inc. The manuscript version is made available under the CC BY-NC-ND 4.0 license.https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/317712026-06-17T12:41:47Z
dc.title.none.fl_str_mv The Pearcey integral in the highly oscillatory region
title The Pearcey integral in the highly oscillatory region
spellingShingle The Pearcey integral in the highly oscillatory region
López García, José Luis
Pearcey integral
Asymptotic expansions
Modified saddle point method
title_short The Pearcey integral in the highly oscillatory region
title_full The Pearcey integral in the highly oscillatory region
title_fullStr The Pearcey integral in the highly oscillatory region
title_full_unstemmed The Pearcey integral in the highly oscillatory region
title_sort The Pearcey integral in the highly oscillatory region
dc.creator.none.fl_str_mv López García, José Luis
Pagola Martínez, Pedro Jesús
author López García, José Luis
author_facet López García, José Luis
Pagola Martínez, Pedro Jesús
author_role author
author2 Pagola Martínez, Pedro Jesús
author2_role author
dc.contributor.none.fl_str_mv Matematika eta Informatika Ingeniaritza
Institute for Advanced Materials and Mathematics - INAMAT2
Ingeniería Matemática e Informática
Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
dc.subject.none.fl_str_mv Pearcey integral
Asymptotic expansions
Modified saddle point method
topic Pearcey integral
Asymptotic expansions
Modified saddle point method
description We consider the Pearcey integral P(x, y) for large values of |y| and bounded values of |x|. The integrand of the Pearcey integral oscillates wildly in this region and the asymptotic saddle point analysis is complicated. Then we consider here the modified saddle point method introduced in [Lopez, Pérez and Pagola, 2009] [4]. With this method, the analysis is simpler and it is possible to derive a complete asymptotic expansion of P(x, y) for large |y|. The asymptotic analysis requires the study of three different regions for separately. In the three regions, the expansion is given in terms of inverse powers of y2/3 and the coefficients are elementary functions of x. The accuracy of the approximation is illustrated with some numerical experiments.
publishDate 2016
dc.date.none.fl_str_mv 2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2454/31771
url https://hdl.handle.net/2454/31771
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv © 2015 Elsevier Inc. The manuscript version is made available under the CC BY-NC-ND 4.0 license.
https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv © 2015 Elsevier Inc. The manuscript version is made available under the CC BY-NC-ND 4.0 license.
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad Pública de Navarra
instname_str Universidad Pública de Navarra
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
repository.name.fl_str_mv
repository.mail.fl_str_mv
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