$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Summary of stability
- Forward Euler is conditionally stable
- \( \Delta t < 2/a \) for avoiding growth
- \( \Delta t\leq 1/a \) for avoiding oscillations
- The Crank-Nicolson is unconditionally stable wrt growth
and conditionally stable wrt oscillations
- \( \Delta t < 2/a \) for avoiding oscillations
- Backward Euler is unconditionally stable
