Application of Asymptotic Expansion for Neumann BC
 

Hi,

I am trying to solve a problem using asymptotic expansion and matching. Suppose it is to solve for y(x) from x = a to x = b. However, unlike in the most common case where y(a) and y(b) are known, in my case I only know the Neumann boundary conditions at a and b (or possibly of the Robin type BC). I have been trying to look for references regarding this, but to no avail so far.

I really appreciate if anyone with experience in it can briefly explain how that can be solved, or point me to some relevant references. Thanks in advance!