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Starting with \( u^0=I \), the simple recursion (28) can be applied repeatedly \( n \) times, with the result that $$ \begin{equation} u^{n} = IA^n,\quad A = \frac{1 - (1-\theta) a\Delta t}{1 + \theta a\Delta t} \tag{29} \end{equation} $$
Such an exact discrete solution is unusual, but very handy for analysis.
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