Listar por tema "Modified saddle point method"
Mostrando ítems 1-6 de 6
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Asymptotic approximation of a highly oscillatory integral with application to the canonical catastrophe integrals
Ferreira González, Chelo
; López García, José Luis 
; Pérez Sinusía, Ester (Wiley, 2023)
Artículo / Artikulua 
We consider the highly oscillatory integral 𝐹(𝑤) ∶= ∫ ∞ −∞ 𝑒𝑖𝑤(𝑡𝐾+2+𝑒𝑖𝜃𝑡𝑝) 𝑔(𝑡)𝑑𝑡 for large positive values of 𝑤, −𝜋 < 𝜃 ≤ 𝜋, 𝐾 and 𝑝 positive integers with 1 ≤ 𝑝 ≤ 𝐾, and 𝑔(𝑡) an entire function. ... -
An asymptotic expansion of the hyberbolic umbilic catastrophe integral
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Springer, 2022)
Artículo / Artikulua
We obtain an asymptotic expansion of the hyperbolic umbilic catastrophe integral Ψ(H) (x,y,z) := ∫∞−∞∫∞−∞exp(i(s3+t3+zst +yt+xs))ds dt for large values of |x| and bounded values of |y| and |z|. The expansion is given ... -
The asymptotic expansion of the swallowtail integral in the highly oscillatory region
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Elsevier, 2018)
Artículo / Artikulua
The mathematical models of many short wavelength phenomena, specially wave propagation and optical diffraction, contain, as a basic ingredient, oscillatory integrals with several nearly coincident stationary phase or ... -
The Pearcey integral in the highly oscillatory region
López García, José Luis ; Pagola Martínez, Pedro Jesús (Elsevier, 2016)
Artículo / Artikulua
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. ... -
The swallowtail integral in the highly oscillatory region II
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Kent State UniversityJohann Radon Institute (RICAM), 2020)
Artículo / Artikulua
We 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., ... -
The swallowtail integral in the highly oscillatory region III
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Taylor & Francis, 2021)
Artículo / Artikulua
We consider the swallowtail integral Ψ(x,y,z):=∫∞−∞ei(t5+xt3+yt2+zt)dt for large values of |z| and bounded values of |x| and |y|. The integrand of the swallowtail integral oscillates wildly in this region and the asymptotic ...
