Asymptotic solution of the Robin problem with a regularly singular point
type: Item
instance of: scholarly article
title: Asymptotic solution of the Robin problem with a regularly singular point
zbMATH Open document ID: 1469.34078
DOI: 10.1134/S1995080221030185
author: Yanyan Li
published in: Lobachevskii Journal of Mathematics
publication date: 2021-05-20T00:00:00Z
review text: In this paper, the authors investigate the Robin boundary-value problem for a singularly perturbed linear inhomogeneous problem \[\begin{aligned} \varepsilon y_{\varepsilon}''(x)+xp(x)y_{\varepsilon}'(x)-q(x)y_{\varepsilon}(x)&=f(x), \quad &&0\leq x\leq 1, \ 0<\varepsilon\ll 1,\\ y_{\varepsilon}(0)-h_1y_{\varepsilon}'(0)&=a, &&0\leq h_1,\\ y_{\varepsilon}(1)+h_2y_{\varepsilon}'(1)&=b, &&0\leq h_2, \end{aligned} \] where \(p(x),q(x)>0\) on \([0,1],\) \(p,q,f\) are of the class \(C^{\infty},\) \(p(0)=1,\) \(q(0)=2,\) and \(a,b,h_1, h_2\) are known constants, \(p(1)+h_2q(1)\neq 0.\) The authors construct a uniform asymptotic expansion of the solution \(y_{\varepsilon}(x)\) of the Robin problem with an arbitrary degree of accuracy on the interval \([0,1]\), when \(\varepsilon\to 0^+\).
reviewed by: Robert Vrabel
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 7350139
zbMATH Keywords: singularly perturbed Robin problem
zbMATH Keywords: asymptotics
zbMATH Keywords: method of boundary layer functions
MaRDI profile type: Publication
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full work available at URL: s1995080221030185
OpenAlex ID: W3159368618
description: scientific article; zbMATH DE number 7350139