Singular perturbation of nonlinear vector boundary value problem
type: Item
instance of: scholarly article
title: Singular perturbation of nonlinear vector boundary value problem
zbMATH Open document ID: 0731.34014
DOI: 10.1007/BF02465731
author: N. E. Zubov
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1988-01-01T00:00:00Z
review text: The authors consider the singularly perturbed boundary value problem for a system of nonlinear vector ordinary differential equations of the form \[ dx/dt=f(x,y,t;\epsilon),\quad \epsilon dy/dt=g(x,y,t;\epsilon), \] \[ a_ 1(\epsilon)x(0,\epsilon)+a_ 2(\epsilon)y(0,\epsilon)=\alpha (\epsilon),\quad b_ 1(\epsilon)x(1,\epsilon)+\epsilon b_ 2(\epsilon)y(1,\epsilon)=\beta (\epsilon). \] The asymptotic expansion of the solution is constructed, the remainder term is estimated. The work of \textit{F. Hoppensteadt} [Commun. Pure Appl. Math. 24, 807-840 (1971; Zbl 0235.34120)] for initial value problem is generalized to the boundary value problems.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34E10
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 4208530
zbMATH Keywords: singular perturbations
zbMATH Keywords: nonlinear vector ordinary differential equations
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: boundary value problems
MaRDI profile type: Publication
cites work: Singular perturbations of a boundary value problem for a system of nonlinear differential equations
cites work: Properties of solutions of ordinary differential equations with small parameters
cites work: Singular perturbations of initial value problems over a finite interval
full work available at URL: https://doi.org/10.1007/bf02465731
OpenAlex ID: W2016646461
description: scientific article; zbMATH DE number 4208530