$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
3rd-order Adams-Bashforth scheme
$$
\begin{equation}
u^{n+1} = u^n + \frac{1}{12}\left( 23f(u^n, t_n) - 16 f(u^{n-1},t_{n-1})
+ 5f(u^{n-2}, t_{n-2})\right)
\tag{45}
\end{equation}
$$
