2nd-order Runge-Kutta scheme

Forward-Euler + approximate Crank-Nicolson: $$\begin{align} u^* &= u^n + \Delta t f(u^n, t_n), \tag{42}\\ u^{n+1} &= u^n + \Delta t \half \left( f(u^n, t_n) + f(u^*, t_{n+1}) \right) \tag{43} \end{align}$$