The swallowtail integral in the highly oscillatory region II

Ferreira, C. (Universidad de Zaragoza) ; Lopez, J.L. ; Sinusia, E.P. (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1553/etna_vol52s88

Año: 2020

Publicado en: ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS 52 (2020), 88-99
ISSN: 1068-9613

Factor impacto JCR: 0.959 (2020)

Categ. JCR: MATHEMATICS, APPLIED rank: 193 / 265 = 0.728 (2020) - Q3 - T3

Factor impacto SCIMAGO: 0.695 - Analysis (Q2)

Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2017-83490-P

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)