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I'm trying to find some tabulated data in some big-and-smart-book with regards to second order central difference of a function of just one variable: f''(x).

I did find formula for 7th order [1], but I need higher orders, like 12 or 15.

thanks a lot!

[1] http://www.holoborodko.com/pavel/numerical-methods/numerical-derivative/central-differences/

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Why would you need high-order? The high-order methods for differences are much more prone to subtractive cancellation. In any event, the formula below the table in your link is a general formula. –  J. M. Dec 22 '11 at 2:17
See this as well. –  J. M. Dec 22 '11 at 2:25
I don't have too much of experience, that's why I was asking, so if 7th order is enough, then i will use it ;). thanks! and thanks for the book! –  LMZ Dec 22 '11 at 2:53
I'd like to point you to dx.doi.org/10.1016/j.jco.2008.05.007 where it is shown that it is possible to get stable behavior of higher order methods if the stepsize is chosen a posteriori. –  Dirk Dec 22 '11 at 7:36

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