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López García, José Luis

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https://academica-e.unavarra.es/handle/2454/49435

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López García

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José Luis

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Estadística, Informática y Matemáticas

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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

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0000-0002-6050-9015

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2369

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2015 - 20162
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Author: López García, José Luis × Author: Pagola Martínez, Pedro Jesús × Subject: Asymptotic expansions × Subject: Pearcey integral ×

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Now showing 1 - 2 of 2
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    PublicationOpen Access
    The Pearcey integral in the highly oscillatory region
    (Elsevier, 2016) López García, José Luis; Pagola Martínez, Pedro Jesús; Matematika eta Informatika Ingeniaritza; Institute for Advanced Materials and Mathematics - INAMAT2; Ingeniería Matemática e Informática; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
    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 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.
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    PublicationOpen Access
    Convergent and asymptotic expansions of the Pearcey integral
    (Elsevier, 2015) López García, José Luis; Pagola Martínez, Pedro Jesús; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
    We consider the Pearcey integral P(x; y) for large values of |x|, x, y ∈ C. We can find in the literature several convergent or asymptotic expansions in terms of elementary and special functions, with different levels of complexity. Most of them are based in analytic, in particular asymptotic, techniques applied to the integral definition of P(x; y). In this paper we consider a different method: the iterative technique used for differential equations in [Lopez, 2012]. Using this technique in a differential equation satisfied by P(x; y) we obtain a new convergent expansion analytically simple that is valid for any complex x and y and has an asymptotic property when |x|→ ∞ uniformly for y in bounded sets. The accuracy of the approximation is illustrated with some numerical experiments and compared with other expansions given in the literature.