$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Explanation of problems with Crank-Nicolson
- \( \Delta t=1.25 \) and \( A=-0.25 \): oscillatory solution
- Never any growing solution