$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\vex}{{v_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\tp}{\thinspace .}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Empirical verification of the truncation error (1)
Ideas:
- Compute \( R^n \) numerically
- Run a sequence of meshes
- Estimate the convergence rate of \( R^n \)
For the Forward Euler scheme:
$$
\begin{equation}
R^n = \lbrack D_t^+\uex + a\uex \rbrack^n
\tag{29}
\tp
\end{equation}
$$
Insert correct \( \uex(t)=Ie^{-at} \) (or use method of manufactured solution
in more general cases).
