000165673 001__ 165673 000165673 005__ 20260113234334.0 000165673 0247_ $$2doi$$a10.1553/etna_vol52s88 000165673 0248_ $$2sideral$$a118834 000165673 037__ $$aART-2020-118834 000165673 041__ $$aeng 000165673 100__ $$0(orcid)0000-0002-3698-6719$$aFerreira, C.$$uUniversidad de Zaragoza 000165673 245__ $$aThe swallowtail integral in the highly oscillatory region II 000165673 260__ $$c2020 000165673 5060_ $$aAccess copy available to the general public$$fUnrestricted 000165673 5203_ $$aWe 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. 000165673 536__ $$9info:eu-repo/grantAgreement/ES/MINECO/MTM2017-83490-P 000165673 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000165673 590__ $$a0.959$$b2020 000165673 591__ $$aMATHEMATICS, APPLIED$$b193 / 265 = 0.728$$c2020$$dQ3$$eT3 000165673 592__ $$a0.695$$b2020 000165673 593__ $$aAnalysis$$c2020$$dQ2 000165673 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000165673 700__ $$aLopez, J.L. 000165673 700__ $$0(orcid)0000-0002-8021-2745$$aSinusia, E.P.$$uUniversidad de Zaragoza 000165673 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000165673 773__ $$g52 (2020), 88-99$$pElectron. trans. numer. anal.$$tELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS$$x1068-9613 000165673 8564_ $$s419440$$uhttps://zaguan.unizar.es/record/165673/files/texto_completo.pdf$$yVersión publicada 000165673 8564_ $$s2124270$$uhttps://zaguan.unizar.es/record/165673/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000165673 909CO $$ooai:zaguan.unizar.es:165673$$particulos$$pdriver 000165673 951__ $$a2026-01-13-22:05:34 000165673 980__ $$aARTICLE