# A Matched Asymptotic Expansion and stretching variables

1. Dec 11, 2017

### joshmccraney

Hi PF!

Regarding matched asymptotic expansions, given an ODE BVP, I have learned a boundary layer can arise, where we need to stretch the independent variable through carefully selection i.e. if $x$ is the independent variable, perhaps $\phi = (1-x)/\epsilon : \epsilon \ll 1$.

Would we ever see a situation where we would have to stretch the dependent variable, say the ODE was over $y(x)$. Something perhaps like $Y = y/\epsilon : \epsilon \ll 1$, as an example.

2. Dec 11, 2017

### joshmccraney

Nevermind, I think it's possible!