0
$\begingroup$

I am searching for a general formula for directly calculating the second, fourth, and sixth derivatives from time series data. Wikipedia has a formula for finding an $n$th order central finite difference. I have searched many places but cannot find it in any reference book. The equation is on a Wikipedia page under "Higher Order Difference.

https://en.wikipedia.org/wiki/Finite_difference

Does anyone know a good reference where one can find a general formula for nth-order finite-difference?

$\endgroup$
3
  • $\begingroup$ You can find "The Calculus of Observations" by Whittaker and Robinson scanned oopy. Chapter III is Central DIfference Formulae and the next Chapter IV is Applications of Difference Formulae. Page 64 and 65 is derivatives in terms of central differences. $\endgroup$
    – Somos
    Commented Jul 20, 2018 at 16:11
  • $\begingroup$ Thank you for the link. I will check. $\endgroup$
    – ACR
    Commented Jul 20, 2018 at 16:48
  • $\begingroup$ There's a paper by Fornberg 1988 titled "Generation of Finite Difference Formulas on Arbitrarily Spaced Grids" ... It's a good place to start. There is also an online calculator (web.media.mit.edu/~crtaylor/calculator.html) and I'm pretty sure they give you the code there if you want to implement it yourself $\endgroup$
    – ThatsRightJack
    Commented Mar 25, 2019 at 2:14

1 Answer 1

Reset to default
0
$\begingroup$

Wikipedia articles come with extensive lists of references. Just picking one promising-looking reference at random (Calculus of Finite Differences by Jordan) I found a section on central differences including the general formulas for $n$th order central differences (they're written in terms of other formulas for forward differences, but putting the pieces together is straightfoward).

$\endgroup$
3
  • 1
    $\begingroup$ Thank you, I checked the first few reference books listed there, but none of them give the exactly show the same relationship as listed there. Also got hold of Jordan's book (1950). The notation is very different. It does not have the same formulae as given in Wikipedia under Higher Order Difference. I am searching this out of curiosity if any other book shows the same equations (written in similar modern notation as in Wikipedia). That section does not have any citation. $\endgroup$
    – ACR
    Commented Jul 20, 2018 at 16:09
  • $\begingroup$ @M.Farooq I don't understand why you need the exact same notation. Surely you can change the notation yourself to suit your needs? Or just use the formula in Wikipedia? $\endgroup$
    – user7530
    Commented Jul 20, 2018 at 16:20
  • 1
    $\begingroup$ Thanks, I just wanted to confirm if the nth order central difference formula in Wikipedia is correct. I am a chemist, trying to implement this in Excel to see higher order even derivatives of a chromatographic peak directly without all derivatives in series (1st, then, 2nd, 3rd and so on). This was the reason for searching a general relation to directly check 2nd, 4th, 6th etc. $\endgroup$
    – ACR
    Commented Jul 20, 2018 at 16:47

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .