Analysis of finite difference equations

Model: $$\begin{equation} u'(t) = -au(t),\quad u(0)=I \end{equation}$$

Method: $$\begin{equation} u^{n+1} = \frac{1 - (1-\theta) a\Delta t}{1 + \theta a\Delta t}u^n \tag{28} \end{equation}$$