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Leading-order error terms in mean values (2)

Geometric mean: [¯u2t,g]n=un12un+12=(un)2+Rn,Rn=14u(tn)2Δt2+14u(tn)u(tn)Δt2+O(Δt4).

Harmonic mean: [¯ut,h]n=un=21un12+1un+12+Rn+12,Rn=u(tn)24u(tn)Δt2+18u(tn)Δt2.

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