$$
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\vex}{{v_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\tp}{\thinspace .}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
$$
Truncation error analysis
- Aim (as always): turn difference operators into derivatives +
truncation error terms
- One-sided forward/backward differences: error \( \Oof{\Delta t} \)
- Linearization of \( |v^{n+1}|v^{n+1} \) to \( |v^n|v^{n+1} \):
error \( \Oof{\Delta t} \)
- All errors are \( \Oof{\Delta t} \)
- First-order scheme? No!
- "Symmetric" use of the \( \Oof{\Delta t} \) building blocks
yields in fact a \( \Oof{\Delta t^2} \) scheme (!)
- Why? See next slide...
