Before revision:  Furthermore, solving ODEs sequentially with small sub-periods with updated initial conditions makes it possible to implement a "substepping method" {\it  for asymptotic expansion in a numerically efficient way.
After revision:  Furthermore, solving ODEs sequentially with small sub-periods with updated initial conditions makes it possible to implement a "substepping method" {\it substepping method for asymptotic expansion in a numerically efficient way.