Loading [MathJax]/extensions/TeX/boldsymbol.js
\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)}

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Truncation error analysis (2)

Resulting truncation error is \Oof{\Delta t^2} : R_u^{n-\half}= \Oof{\Delta t^2}, \quad R_v^n = \Oof{\Delta t^2}\tp

Observation.

Comparing The schemes (50)-(51) and (46)-(47) are equivalent. Therefore, the forward/backward scheme with ad hoc linearization is also \Oof{\Delta t^2} !

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