$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\tp}{\thinspace .}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Phase plane plot of the numerical solutions
Note: CrankNicolson in Odespy leads to the name MidpointImplicit in plots.
