$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\tp}{\thinspace .}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
\newcommand{\dfc}{\alpha} % diffusion coefficient
$$
Damping of a discontinuity; Crank-Nicolson scheme
Discrete model:
$$ [D_t u = \dfc D_xD_x\overline{u}^t]^n_i $$
results in a tridiagonal linear system
