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)}

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The truncation error for other schemes

Backward Euler: R^n \approx -\half\uex''(t_n)\Delta t

Crank-Nicolson: R^{n+\half} \approx \frac{1}{24}\uex'''(t_{n+\half})\Delta t^2

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