Simplest method: run a few algorithmic steps by hand

Use a calculator ($I=0.1$, $\theta=0.8$, $\Delta t =0.8$): $$A\equiv \frac{1 - (1-\theta) a\Delta t}{1 + \theta a \Delta t} = 0.298245614035$$ $$\begin{align*} u^1 &= AI=0.0298245614035,\\ u^2 &= Au^1= 0.00889504462912,\\ u^3 &=Au^2= 0.00265290804728 \end{align*}$$

See the function verify_three_steps in decay_verf1.py.