First-order general differential equation for multi-level asymptotics at higher levels and recurrence relationship of singulants
type: Item
instance of: scholarly article
title: First-order general differential equation for multi-level asymptotics at higher levels and recurrence relationship of singulants
zbMATH Open document ID: 1492.34089
author: Fatih Say
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2022-02-03T00:00:00Z
review text: In this article, the author is interested in the singularly perturbed first-order ordinary differential equation \[ \varepsilon\dfrac{dy}{dz}+A(z)y=f(z) \] with a small positive parameter \(\varepsilon\). He investigates the asymptotic behavior of its formal power series solution in \(\varepsilon\), and aims to locate and study its Stokes and anti-Stokes lines. The approach developed by the author is based on the method of multi-level asymptotics introduced in [\textit{F. Say}, Exponential asymptotics: multi-level asymptotics of model problems. University of Nottingham (PhD Thesis) (2016)], a method which is similar to the methods already used in hyperasymptotics (see [\textit{M. V. Berry} and \textit{C. J. Howls}, Proc. R. Soc. Lond., Ser. A 430, No. 1880, 653--668 (1990; Zbl 0745.34052)] for instance).
reviewed by: Pascal Remy
Mathematics Subject Classification ID: 34M40
Mathematics Subject Classification ID: 34M60
zbMATH DE Number: 7468760
zbMATH Keywords: Multi-level asymptotics
zbMATH Keywords: singularly perturbed differential equation
zbMATH Keywords: Stokes lines
zbMATH Keywords: Anti-Stokes lines
Wikidata QID: Q114013402
MaRDI profile type: Publication
full work available at URL: crmath.264
OpenAlex ID: W4206352773
cites work: Stokes' phenomenon; smoothing a Victorian discontinuity
cites work: Uniform asymptotic smoothing of Stokes’s discontinuities
cites work: Waves near Stokes lines
cites work: Stokes’s phenomenon for superfactorial asymptotic series
cites work: Hyperasymptotics
cites work: Exponential asymptotics of a fifth-order partial differential equation
cites work: A comparison of numerical and analytical methods for the reduced wave equation with multiple spatial scales
cites work: A hyperasymptotic perturbative method for computing the radiation coefficient for weakly nonlocal solitary waves
cites work: The devil's invention: Asymptotic, superasymptotic and hyperasymptotic series
cites work: Hyperasymptotics and the Linear Boundary Layer Problem: Why Asymptotic Series Diverge
cites work: On the non-universality of the error function in the smoothing of stokes discontinuities
cites work: Why is a shock not a caustic? The higher-order Stokes phenomenon and smoothed shock formation
cites work: Exponential asymptotics and Stokes lines in nonlinear ordinary differential equations
cites work: On the Theory of Complex Rays
cites work: Exponential asymptotics and Stokes lines in a partial differential equation
cites work: Exponential Asymptotics for Thin Film Rupture
cites work: Q4765553
cites work: Q3245431
cites work: Q3997900
cites work: On the higher–order Stokes phenomenon
cites work: Exponentially accurate solution tracking for nonlinear ODEs, the higher order Stokes phenomenon and double transseries resummation
cites work: Nonlinear q-Stokes phenomena for q-Painlevé I
cites work: Asymptotics beyond all orders and Stokes lines in nonlinear differential-difference equations
cites work: Error estimates for asymptotic representations of integrals
cites work: Smoothing of Stokes discontinuities
cites work: Stokes Phenomenon and Matched Asymptotic Expansions
cites work: Q3126395
cites work: Q3842162
DOI: 10.5802/CRMATH.264
describes a project that uses: Digital Library of Mathematical Functions
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description: scientific article; zbMATH DE number 7468760