$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\vex}{{v_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\tp}{\thinspace .}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Truncation errors in the initial condition
- Initial conditions: \( u(0)=I \), \( u'(0)=V \)
- Need discretization of \( u'(0) \)
- Standard, centered difference: \( [D_{2t} u=V]^0 \), \( R^0=\Oof{\Delta t^2} \)
- Simpler, forward difference: \( [D_t^+u=V]^0 \), \( R^0=\Oof{\Delta t} \)
- Does the lower order of the forward scheme impact the order of
the whole simulation?
- Answer: run experiments!
