Practice question · Multiple choice
Euler's method has local error O(h²) per step and global error O(h). Where does the lost order go?
Hints
- How many steps does it take to cross a fixed interval with step size h?
- Multiply the per-step error by the number of steps.
Show the answer
C. Into the number of steps, about 1/h of them over a fixed interval
Why
h² per step times 1/h steps is h, the accumulation costs exactly one order. That is why Euler is first-order and halving the step only halves the error, and why RK4 evaluates the derivative four times per step to reach O(h⁴), a far better return on the extra work.
Practise The Fundamental Theorem of Calculus
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