$$ \newcommand{\uex}{{u_{\small\mbox{e}}}} \newcommand{\half}{\frac{1}{2}} \newcommand{\tp}{\thinspace .} \newcommand{\Oof}[1]{\mathcal{O}(#1)} $$

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Algorithm

  1. \( u^0=I \)
  2. compute \( u^1 \) (formula depends on linear/quadratic damping)
  3. for \( n=1,2,\ldots,N_t-1 \):
    1. compute \( u^{n+1} \) from formula (depends on linear/quadratic damping)

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