二阶线性向量方程初值问题的奇摄动解

本文应用边界层校正法讨论下述带小参数的二阶线性向量方程初值问题: εy″(x,ε)+P(ε)y′(x,ε)+Q(ε)y(x,ε)=f(x) y(0,ε)=a(ε) y′(0,ε)=b(ε)在一定条件下,获得了解的一致有效渐近展开,并给出了余项估计。

Singular Perturbation of lnitial Value Problem for A Vector Second Order Linear Differential Equation

Using the method of boundary layer correcting we consider singularperturbation of initial value problem for following vector second order lineardifferential equation: εy″(x, ε) + P(ε)y′(x,ε) + Q(ε)y(x, ε) = f(x) y (0, ε) = a (ε) y′(0, ε) = b (ε) Under certain conditions, the asymptotic expansion of solution of orderN is constructed, and the remainder is estimated.