Exercise · ZW-LOCAL-AND-GLOBAL-ERROR-005 · ★☆☆ Basic
What best describes how local errors build up into the global error?
Choose one option.
Show answer
- A. They add up or propagate across the steps
Explanation
Each local error carries into later steps and combines with the others, so the global error grows with the number of steps.
Review the concept: Local and global error
The local error is the difference between the exact ODE solution over one step and the method's approximation starting from the exact value.
\[e_{n+1}=y(t_{n+1})-y_{n+1}\]
More practice problems: local and global error
- ZW-LOCAL-AND-GLOBAL-ERROR-001 What does the local error measure in a numerical ODE method?
- ZW-LOCAL-AND-GLOBAL-ERROR-002 What does the global error measure in a numerical ODE method?
- ZW-LOCAL-AND-GLOBAL-ERROR-003 If a method's local error is O(h^2), what order does the global error typically have?
- ZW-LOCAL-AND-GLOBAL-ERROR-004 With Euler's method, what is the local error when computing y_n+1 from y(t_n)?
- ZW-LOCAL-AND-GLOBAL-ERROR-006 For y'=y, y(0)=1, and h=0.1, what is approximately the local error of the first Euler step?
- ZW-LOCAL-AND-GLOBAL-ERROR-007 If halving h roughly halves the global error of Euler's method, what is the order of the global err…
- ZW-LOCAL-AND-GLOBAL-ERROR-008 If the local error of one step is C h^3, roughly how many steps accumulate over the interval [0,1]?
- ZW-LOCAL-AND-GLOBAL-ERROR-009 A method has local error O(h^2). If h goes from 0.1 to 0.05, how does the global error change appro…
← ZW-LOCAL-AND-GLOBAL-ERROR-004 ZW-LOCAL-AND-GLOBAL-ERROR-006 →