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Jan 17 at 4:25 comment added helloworld922 I would agree that Runge's phenomenon can reduce the order of convergence especially for high order multi-dimensional FD. I don't think it would prevent overall convergence, though (at least with exact real mathematics, not sure when you introduce floating points).
Jan 16 at 19:26 comment added ConvexHull @helloworlds I think this does not hold in general. Higher-order finite differences, e.g. one-sided and equidistant, may lack of the Runge's phenomenon.
Jan 16 at 7:55 vote accept FriendlyNeighborhoodEngineer
Jan 16 at 2:31 history edited helloworld922 CC BY-SA 4.0
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Jan 16 at 2:24 history answered helloworld922 CC BY-SA 4.0