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Truncation error analysis (1)

Resulting scheme: [Dtu]n12=vn12,[Dtv]n=1m(F(tn)β|vn12|vn+12s(un)).

The truncation error in each equation is found from [Dtue]n12=ve(tn12)+Rn12u,[Dtve]n=1m(F(tn)β|ve(tn12)|ve(tn+12)s(un))+Rnv. Using (3)-(4) for derivatives and (21)-(22) for the geometric mean: ue(tn12)+124ue(tn12)Δt2+O(Δt4)=ve(tn12)+Rn12u, and ve(tn)=1m(F(tn)β|ve(tn)|ve(tn)+O(Δt2)s(un))+Rnv.

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