Practice question · Multiple choice
A convergence study halves the step size and checks the error falls by the expected factor. Why is that a stronger check than comparing against a known answer?
Hints
- Simulations exist for problems with no known answer. Ask what can still be checked.
- A wrong convergence rate reveals what a single wrong number does not.
Show the answer
A. Because it tests the method's order, not one output
Why
The relationship between step size and error is predicted by theory independently of the answer, so a second-order method reducing error by 2 rather than 4 signals a bug even when every output looked plausible. Boundary conditions applied one cell off produce exactly that signature.
Practise Multivariable Calculus and Gradients
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