Now consider a forward difference: u′(tn)≈[D+tu]n=un+1−unΔt. Define the truncation error: Rn=[D+tu]n−u′(tn). Expand un+1 in a Taylor series around tn, u(tn+1)=u(tn)+u′(tn)Δt+12u″(tn)Δt2+O(Δt3). We get R=12u″(tn)Δt+O(Δt2).