On a singular perturbation problem with two second-order turning points
type: Item
instance of: scholarly article
title: On a singular perturbation problem with two second-order turning points
zbMATH Open document ID: 1103.34047
author: Heping Yang
published in: Journal of Computational and Applied Mathematics
publication date: 2006-03-24T00:00:00Z
review text: The paper deals with the singularly perturbed equation \[ \varepsilon p(x)u_{xx} + 2(x-a)(b-x)u_x -2su = 0, \;x \in (0,1), \tag{1} \] where \(0 < a < b < 1,\) \(\varepsilon\) is small positive parameter and \(s = \text{const}.\) The functions \(p(x)\) and \(q(x)\) are strictly positive and sufficiently smooth on the interval \((0,1).\) Equation (1) has two second-order turning points \(x=a\) and \(x=b\) on \((0,1).\) The author gives uniform asymptotic solutions for (1) on the whole interval \((0,1).\) The solutions obtained are applied to the study of the boundary value problem \(u(0)=k_1, u(1)=k_2\) for equation (1).
reviewed by: Victor I. Tkachenko
Mathematics Subject Classification ID: 34E20
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 5015182
zbMATH Keywords: singular perturbation
zbMATH Keywords: turning point
zbMATH Keywords: asymptotic solution
MaRDI profile type: Publication
full work available at URL: j.cam.2005.01.040
OpenAlex ID: W1971463232
cites work: Q3661894
cites work: Boundary Layer Problems Exhibiting Resonance
cites work: Q3207312
cites work: Sufficient Conditions for Ackerberg–O’Malley Resonance
cites work: On a Differential Equation of Boundary Layer Type
cites work: Q3682833
cites work: A singular perturbation problem with a turning point
cites work: Two Turning Points of Second Order
cites work: On an internal boundary layer problem
cites work: On a Boundary Layer Problem
cites work: On the Ackerberg-O'Malley Resonance
DOI: 10.1016/J.CAM.2005.01.040
description: scientific article; zbMATH DE number 5015182