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Computation of the truncation error

Tool: Taylor expand ue around the point where the ODE is sampled (here tn) ue(tn+1)=ue(tn)+ue(tn)Δt+12ue(tn)Δt2+ Inserting this Taylor series in (31) gives Rn=ue(tn)+12ue(tn)Δt++aue(tn) Now, ue solves the ODE ue=aue, and then Rn12ue(tn)Δt This is a mathematical expression for the truncation error.

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