Processing math: 100%
Computation of the truncation error
- The residual Rn is the truncation error.
- How does Rn vary with Δt?
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
Rn≈12ue″(tn)Δt
This is a mathematical expression for the truncation error.