Smoothness of function and finite difference method for computing its (first) derivative

Question

I wonder whether a finite difference method for computing the first derivative of function, just needs that it belongs to (differentiability) class $C^{1}$. But I read that for case of central difference difference, the function should belong to, at least, $C^{2}$. Is it true?

Where did you read that? Link? – Demetri Pananos Sep 28 '16 at 15:37 — Demetri Pananos, Sep 28 '16 at 15:37

score 0 · Answer 1 · answered Jul 27 '19 at 11:37

0

It depends on the order of derivation in Taylor series approximation. If you use centered differential formula for 2nd derivatives, of course the function should be of class $C^2$.

answered Jul 27 '19 at 11:37

S. Maths

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Smoothness of function and finite difference method for computing its (first) derivative

1 Answers1