$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Algorithm
- Store \( u^n \), \( n=0,1,\ldots,N_t \) in an array
u.
- Algorithm:
- initialize \( u^0 \)
- for \( t=t_n \), \( n=1,2,\ldots,N_t \): compute \( u_n \) using
the \( \theta \)-rule formula
