Loading [MathJax]/extensions/TeX/boldsymbol.js
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
2nd-order Runge-Kutta scheme
Forward-Euler + approximate Crank-Nicolson:
\begin{align}
u^* &= u^n + \Delta t f(u^n, t_n),
\tag{42}\\
u^{n+1} &= u^n + \Delta t \half \left( f(u^n, t_n) + f(u^*, t_{n+1})
\right)
\tag{43}
\end{align}
