Listar por tema "Asymptotic expansions"
Mostrando ítems 1-13 de 13
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Asymptotic and convergent expansions for solutions of third-order linear differential equations with a large parameter
Ferreira González, Chelo
; López García, José Luis 
; Pérez Sinusía, Ester (Shanghai Normal UniversityWilmington Scientific Publisher, 2018)
Artículo / Artikulua 
In previous papers [6–8,10], we derived convergent and asymptotic expansions of solutions of second order linear differential equations with a large parameter. In those papers we generalized and developed special cases not ... -
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. ... -
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 ... -
Asymptotic expansions for Moench's integral transform of hydrology
López García, José Luis ; Pagola Martínez, Pedro Jesús ; Pérez Sinusía, Ester (MDPI, 2023)
Artículo / Artikulua
Theis' theory (1935), later improved by Hantush & Jacob (1955) and Moench (1971), is a technique designed to study the water level in aquifers. The key formula in this theory is a certain integral transform H[g](r,t) of ... -
Convergent and asymptotic expansions of the Pearcey integral
López García, José Luis ; Pagola Martínez, Pedro Jesús (Elsevier, 2015)
Artículo / Artikulua
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 ... -
Convergent and asymptotic methods for second-order difference equations with a large parameter
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Springer, 2018)
Artículo / Artikulua
We consider the second-order linear difference equation y(n+2)−2ay(n+1)−Λ2y(n)=g(n)y(n)+f(n)y(n+1) , where Λ is a large complex parameter, a≥0 and g and f are sequences of complex numbers. Two methods are proposed to find ... -
New asymptotic expansion and error bound for Stirling formula of reciprocal Gamma function
Pagola Martínez, Pedro Jesús (Ele-Math, 2018)
Artículo / Artikulua
Studying the problem about if certain probability measures are determinate by its moments [4, 8, 10] is useful to know the asymptotic behavior of the probability densities for large values of argument. This requires, ... -
New series expansions for the ℋ-function of communication theory
Ferreira, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Taylor & Francis, 2023)
Artículo / Artikulua
TheH-function of communication theory plays an important role inthe error rate analysis in digital communication with the presenceof additive white Gaussian noise (AWGN) and generalized multipathfading conditions. In this ... -
On a modifcation of Olver's method: a special case
Ferreira González, Chelo; López García, José Luis ; Pérez Sinusía, Ester (Springer US, 2016)
Artículo / Artikulua
We consider the asymptotic method designed by Olver (Asymptotics and special functions. Academic Press, New York, 1974) for linear differential equations of the second order containing a large (asymptotic) parameter : ... -
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. ... -
A simplification of the stationary phase method: application to the Anger and Weber functions
López García, José Luis (Kent State UniversityJohann Radon Institute (RICAM), 2017)
Artículo / Artikulua
The main difficulty in the practical use of the stationary phase method in asymptotic expansions of integrals is originated by a change of variables. The coefficients of the asymptotic expansion are the coefficients of the ... -
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 ...
