Comparing amplification factors

$u^{n+1}$ is an amplification $A$ of $u^n$: $$u^{n+1} = Au^n,\quad A = \frac{1 - (1-\theta) a\Delta t}{1 + \theta a\Delta t}$$

The exact solution is also an amplification: $$u(t_{n+1}) = \Aex u(t_n), \quad \Aex = e^{-a\Delta t}$$

A possible measure of accuracy: $\Aex - A$