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