On the asymptotics of the solution of a system of linear equations with two small parameters
type: Item
instance of: scholarly article
title: On the asymptotics of the solution of a system of linear equations with two small parameters
zbMATH Open document ID: 1170.34039
DOI: 10.1134/S0012266108060025
author: A. R. Danilin
author: O. O. Kovrizhnykh
published in: Differential Equations
publication date: 2009-03-26T00:00:00Z
review text: The following Cauchy problem for a system of two linear ordinary differential equations with two independent small parameters multiplying the derivatives is considered: \[ \varepsilon\frac{dx}{dt}=a(t)x+b(t)y+f(t), \mu\frac{dy}{dt}=c(t)x+d(t)y+g(t)\tag{1} \] \[ x|_{t=0}=x^0, y|_{t=0}=y^0,\tag{2} \] where \(a(t),b(t),c(t),d(t),f(t),\) and \(g(t)\) are sufficiently smooth functions of \(t\in[0,T]\) satisfying the conditions \[ a(t)<0, d(t)<0, D(t)=a(t)d(t)-b(t)c(t)>0\tag{3} \] and \(\varepsilon>0\) and \(\mu>0\) are small parameters. Estimates fot the terms in the asymptotic expansion of the solution are obtained. Recursion formulas for the efficient computation of terms of the inner expansion are given.
reviewed by: Vasile Dragan
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34E13
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 5533503
zbMATH Keywords: singular perturbations
zbMATH Keywords: linear differential equations
zbMATH Keywords: asymptotic expansion of solutions
zbMATH Keywords: inner expansions
MaRDI profile type: Publication
cites work: Q4003188
description: scientific article; zbMATH DE number 5533503