A novel method for a class of nonlinear singular perturbation problems
type: Item
instance of: scholarly article
title: A novel method for a class of nonlinear singular perturbation problems
zbMATH Open document ID: 1069.65088
author: Lei Wang
published in: Applied Mathematics and Computation
publication date: 2004-11-23T00:00:00Z
review text: The problem under consideration is the singularly perturbed boundary value problem \[ \varepsilon y'' + f(x,y)y' + g(x,y) = 0, \quad 0 < x < 1, \quad y(0) = \alpha , \quad y(1) = \beta \] The solution of the problem is constructed as the sum \[ y(x) = U(x) + V(x/\varepsilon) + O(\varepsilon ). \] The regular part \(U\) is defined by the initial value problem \[ f( x,U )U' + g(x,U) = 0,\quad U(1) = \beta , \] and the boundary layer function \(V\) is defined by the correction problem \[ V'' + f(0,U(0) + V)V' = 0, \quad V(0) = \alpha - U(0), \quad \lim_{t \to \infty } V(t) = 0. \] To solve the last problem, the author suggests a shooting technique based on the series method and Padé approximation. Numerical experiments are presented.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 2118013
zbMATH Keywords: boundary layer
zbMATH Keywords: series method
zbMATH Keywords: Padé approximation
zbMATH Keywords: singular perturbation
zbMATH Keywords: shooting method
zbMATH Keywords: boundary value problem
zbMATH Keywords: numerical experiments
reviewed by: Vladimir Gorbunov
MaRDI profile type: Publication
full work available at URL: j.amc.2003.06.010
OpenAlex ID: W1968315702
cites work: A study on a boundary layer equation arising in an incompressible fluid
cites work: A boundary value method for a class of nonlinear singular perturbation problems
cites work: Q3207312
DOI: 10.1016/J.AMC.2003.06.010
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description: scientific article; zbMATH DE number 2118013