摘要
今研究一阶非线性向量微分方程初值问题:εy′=f(t,y,ε),(1)y(0,ε)=A(ε),(2)其可ε>0为小参数.y=(y_1,y_2,…,y_n)为 n 维向量函数.Howes 等人研究了一类高阶非线性标量微分方程的奇摄动问题.对于二阶非线性向量微分方程的奇摄动,也在许多文献中不同程度地研究过(例如[2],[3]).本文是研究更广泛的一类一阶非线性向量微分方程的奇摄动,提供了构造相应初值问题(1),(2)
In this paper the initial value problem of first order nonlinear vector differentialequations:εy=f(t,y,ε),y(0,ε)=A(ε),where ε>0 is a small parameter,isconsidered.Under suitable conditions,we can prove that the solution y≡(y_1,…,y_(?))of the initial value problem holds the uniformly valid asymptotic expansion:(?)=1,2,…,n;0<ε(?)1,where m is an arbitrary positive integer,sum from (?)=0 to m y_(ji)ε~i is an m-th order approximation ofthe outer solution of the original problem and sum from (?)=0 to m u_(ji)ε~i is an initial layer correctionof the solution.
出处
《应用数学学报》
CSCD
北大核心
1989年第4期397-402,共6页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金资助的课题
