Solution
= Solution
The first scheme has
$$
H(\theta)=1+\mu(1-e^{-i\theta}).
$$
At $\theta=\pi$,
$$
|H(\pi)|=1+2\mu.
$$
Since the <Courant number> obeys $\mu\geq0$, stability therefore holds exactly for
$$
\boxed{\mu=0}.
$$
= Solution
The first scheme has
$$
H(\theta)=1+\mu(1-e^{-i\theta}).
$$
At $\theta=\pi$,
$$
|H(\pi)|=1+2\mu.
$$
Since the <Courant number> obeys $\mu\geq0$, stability therefore holds exactly for
$$
\boxed{\mu=0}.
$$