$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
The filtered Leapfrog scheme
After computing \( u^{n+1} \), stabilize Leapfrog by
$$
\begin{equation}
u^n\ \leftarrow\ u^n + \gamma (u^{n-1} - 2u^n + u^{n+1})
\tag{41}
\end{equation}
$$
