$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\tp}{\thinspace .}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Algorithm
- \( u^0=I \)
- compute \( u^1 \) (formula depends on linear/quadratic damping)
- for \( n=1,2,\ldots,N_t-1 \):
- compute \( u^{n+1} \) from formula (depends on linear/quadratic damping)