Lets consider following differential equation,
$\epsilon \frac{dy}{dt} = ....$
In principle one can use Method of matched asymptotic expansion or Method of multiple scales to solve such singular problems. But these techniques work on inherent assumption on $\epsilon \ll 1$ or more precisely $\epsilon \ll \frac{dy}{dt}$ for all times.
Now if in some time domain the later condition is not satisfied, the standard expansion breaksdown. What is the remedy to deal with such problems?