From what I know, a stability condition depends on the eigenvalues of a matrix and CFL condition involves a time component. Say I have a system $$Au=f$$ but then add in a time component so that I have $$\frac{du}{dt}+Au=f$$
Is the only real difference that I have the consider the adjusted eigenvalues of the second equation? In particular, if I am using forward Euler to approximate the time component, what does my CFL condition look like? Essentially, I am just confused as to how I get the bound for a CFL condition and how it differs from a stability condition.