I have a code for MultiGrid in 1D.
The code solves the Poisson equation with the central difference approximation. $uL-2u+uR=f$.
I would like to generalize this approach and use it for the $uL-a u+uR=f$, (with $a \leftarrow 2-\epsilon$). The code works fine if $|\epsilon|>0.1$.
However it blows up if I choose $\epsilon =0.01$ it blows up. This happens with both cell center or cell vertex formulation. Is there anyway to fix this issue? Thanks for your helps