165673 20260113234334.0 doi 10.1553/etna_vol52s88 sideral 118834 ART-2020-118834 eng Ferreira, C. Universidad de Zaragoza (orcid)0000-0002-3698-6719 The swallowtail integral in the highly oscillatory region II 2020 We analyze the asymptotic behavior of the swallowtail integral ¿&inf;-&inf; ei(t5+xt3+yt2+zt)dt for large values of jyj and bounded values of |x| and |z|. We use the simplified saddle point method introduced in [Lopez et al., J. Math. Anal. Appl., 354 (2009), pp. 347-359]. 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 fixed x and z. There are four Stokes lines in the sector (-p, p] that divide the complex y-plane into four sectors in which the swallowtail integral behaves differently 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 y1/2. The other one is given in terms of an asymptotic sequence whose terms are of the order of inverse powers of y1/9 when |y| ¿ &inf;, and it is multiplied by an exponential factor that behaves differently in the four mentioned sectors. Some numerical experiments illustrate the accuracy of the approximation. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/MINECO/MTM2017-83490-P info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 0.959 2020 MATHEMATICS, APPLIED 193 / 265 = 0.728 2020 Q3 T3 0.695 2020 Analysis 2020 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Lopez, J.L. Sinusia, E.P. Universidad de Zaragoza (orcid)0000-0002-8021-2745 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 52 (2020), 88-99 Electron. trans. numer. anal. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS 1068-9613 419440 http://zaguan.unizar.es/record/165673/files/texto_completo.pdf Versión publicada 2124270 http://zaguan.unizar.es/record/165673/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:165673 articulos driver 2026-01-13-22:05:34 ARTICLE