$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
The true/global error at a point
- The error in \( A \) reflects the local error when going from one
time step to the next
- What is the global (true) error at \( t_n \)?
\( e^n = \uex(t_n) - u^n = Ie^{-at_n} - IA^n \)
- Taylor series expansions of \( e^n \) simplify the expression
