000165525 001__ 165525 000165525 005__ 20260113221443.0 000165525 0247_ $$2doi$$a10.1080/17476933.2020.1868447 000165525 0248_ $$2sideral$$a122527 000165525 037__ $$aART-2022-122527 000165525 041__ $$aeng 000165525 100__ $$0(orcid)0000-0002-3698-6719$$aFerreira, C.$$uUniversidad de Zaragoza 000165525 245__ $$aThe swallowtail integral in the highly oscillatory region III 000165525 260__ $$c2022 000165525 5060_ $$aAccess copy available to the general public$$fUnrestricted 000165525 5203_ $$aWe consider the swallowtail integral (Formula presented.) for large values of (Formula presented.) and bounded values of (Formula presented.) and (Formula presented.). 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 (Formula presented.) for large (Formula presented.) and fixed x and y. The asymptotic analysis requires the study of three different regions for (Formula presented.) separated by three Stokes lines in the sector (Formula presented.). 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 (Formula presented.) when (Formula presented.), 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. 000165525 536__ $$9info:eu-repo/grantAgreement/ES/MINECO/MTM2017-83490-P 000165525 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es 000165525 590__ $$a0.9$$b2022 000165525 591__ $$aMATHEMATICS$$b147 / 329 = 0.447$$c2022$$dQ2$$eT2 000165525 592__ $$a0.457$$b2022 000165525 593__ $$aAnalysis$$c2022$$dQ2 000165525 593__ $$aApplied Mathematics$$c2022$$dQ2 000165525 593__ $$aComputational Mathematics$$c2022$$dQ3 000165525 593__ $$aNumerical Analysis$$c2022$$dQ3 000165525 594__ $$a1.8$$b2022 000165525 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000165525 700__ $$aLópez, J.L. 000165525 700__ $$0(orcid)0000-0002-8021-2745$$aPérez Sinusía, E.$$uUniversidad de Zaragoza 000165525 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000165525 773__ $$g67, 5 (2022), 1262-1272$$pCOMPLEX VARIABLES AND ELLIPTIC EQUATIONS$$tCOMPLEX VARIABLES AND ELLIPTIC EQUATIONS$$x1747-6933 000165525 8564_ $$s508737$$uhttps://zaguan.unizar.es/record/165525/files/texto_completo.pdf$$yPostprint 000165525 8564_ $$s1251799$$uhttps://zaguan.unizar.es/record/165525/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000165525 909CO $$ooai:zaguan.unizar.es:165525$$particulos$$pdriver 000165525 951__ $$a2026-01-13-22:10:33 000165525 980__ $$aARTICLE