$$ \newcommand{\uex}{{u_{\small\mbox{e}}}} \newcommand{\Aex}{{A_{\small\mbox{e}}}} \newcommand{\half}{\frac{1}{2}} \newcommand{\tp}{\thinspace .} \newcommand{\Oof}[1]{\mathcal{O}(#1)} \newcommand{\dfc}{\alpha} % diffusion coefficient $$
Crank-Nicolson applied to a plug profile
Crank-Nicolson never blows up, so any \( F \) can be used (modulo loss of accuracy).
\( N_x=50 \). \( F=5 \) gives instabilities.
\( N_x=50 \). \( F=0.5 \) gives a smooth solution.
