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} !