$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Stability
Since \( u^n\sim A^n \),
- \( A < 0 \) gives a factor \( (-1)^n \) and oscillatory solutions
- \( |A|>1 \) gives growing solutions
- Recall: the exact solution is monotone and decaying
- If these qualitative properties are not met, we say that the
numerical solution is unstable
