$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Step 1: Discretizing the domain
\( u^n \) is a mesh function, defined at the mesh points \( t_n \), \( n=0,\ldots,N_t \)
only.
