Practice question · Multiple choice
A physics engine integrating with a smaller timestep is more accurate and eventually gets worse below a certain step size. Why does refinement stop helping?
Hints
- Sketch two curves against step size: one falling, one rising. Where is their sum smallest?
- Halving the step doubles the number of arithmetic operations. What does each one do?
Show the answer
D. Because truncation error falls with the step while round-off grows
Why
Two errors move oppositely, so their sum has a minimum, and pushing past it makes the answer worse while costing more. 'More refinement is better' holds only until the arithmetic becomes the limiting factor, which is one of the least intuitive facts in numerical work.
Practise Applications of Derivatives
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