Loading [MathJax]/extensions/TeX/boldsymbol.js
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
Truncation error
- How good is the discrete equation?
- Possible answer: see how well \uex fits the discrete equation
\lbrack D_t u = -au\rbrack^n
i.e.,
\frac{u^{n+1}-u^n}{\Delta t} = -au^n
Insert \uex (which does not in general fulfill this equation):
\begin{equation}
\frac{\uex(t_{n+1})-\uex(t_n)}{\Delta t} + a\uex(t_n) = R^n \neq 0
\tag{31}
\end{equation}
