Ferreira González, CheloLópez García, José LuisPérez Sinusía, Ester2021-09-062021-09-0620201068-961310.1553/etna_vol52s88https://academica-e.unavarra.es/handle/2454/40433We 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.13 p.application/pdfeng© 2020, Kent State UniversitySwallowtail integralAsymptotic expansionsModified saddle point methodinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessAcceso abierto / Sarbide irekia