An exercise I am working on states;
Find formally the asymptotic error expansion for the scheme you pro- pose in #A3. This will involve two types of terms $U = u + h_4 ( c(x) + Aκ_j + Bκ_{N−j} )$ where $c(x)$ is a smooth function that solves a BVP and $|κ| < 1$ is a root of $D2κ_j = 0$. The terms involving κ are called numerical boundary layers.
I tried searching up the term "numerical boundary layer" and I came up with nothing.
The "A3" portion refers to a modification of finite difference coeffcients to handle skewed finite differences at the boundary.
i.e. this stencil times $h^2$:
$$\frac{11}{12}, \frac{-5}{3}, \frac{1}{2}, \frac{1}{3}, \frac{-1}{12}$$
will replace the regular 5 point stencil. In general I just don't understand the question.