The Pearcey integral in the highly oscillatory region

José L. López and Pedro J. Pagola

Applied Mathematics and Computation, 2016, vol. 275, issue C, 404-410

Abstract: We consider the Pearcey integral P(x, y) for large values of |y| and bounded values of |x|. The integrand of the Pearcey integral oscillates wildly in this region and the asymptotic saddle point analysis is complicated. Then we consider here the modified saddle point method introduced in [Lopez, Pérez and Pagola, 2009] [4]. With this method, the analysis is simpler and it is possible to derive a complete asymptotic expansion of P(x, y) for large |y|. The asymptotic analysis requires the study of three different regions for argy separately. In the three regions, the expansion is given in terms of inverse powers of y2/3 and the coefficients are elementary functions of x. The accuracy of the approximation is illustrated with some numerical experiments.

Keywords: Pearcey integral; Asymptotic expansions; Modified saddle point method (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:275:y:2016:i:c:p:404-410

DOI: 10.1016/j.amc.2015.11.080

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