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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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    I'd like to point you to http://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.2011-12-22

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