$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\tp}{\thinspace .}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Initial conditions
$$
\begin{align*}
u^0 &= I\\
v^{\half} &= V - \half\Delta t\omega^2I
\end{align*}
$$
