I've been discretizing PDEs and formulating $Ax=b$ systems, and yet I don't really know what the $A$ and $b$ are in words.
I occasionally call the $A$ matrix the "Jacobian matrix," but for linear PDEs, "Jacobian" doesn't make sense, so I call it the "differential operator matrix." Is there a standard name for this $A$ matrix?
For the $b$ vector, I call it the forcing vector, but I don't know if that is correct either.
Are there standard names for both of these variables after applying a discretization to a PDE (whether linear or nonlinear)?