$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\tp}{\thinspace .}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Verification
- Constant solution \( \uex = I \) (\( V=0 \)) fulfills the ODE problem
and the discrete equations. Ideal for debugging!
- Linear solution \( \uex = Vt+I \) fulfills the ODE problem and
the discrete equations.
- Quadratic solution \( \uex = bt^2 + Vt + I \) fulfills the ODE
problem and the discrete equations with linear damping, but not
for quadratic damping.
A special discrete source term can allow \( \uex \) to also fulfill
the discrete equations with quadratic damping.
