       Re: Numerical Differentiation

• To: mathgroup at smc.vnet.net
• Subject: [mg4277] Re: Numerical Differentiation
• From: sfpse at u.washington.edu (Russell Brunelle)
• Date: Sat, 29 Jun 1996 03:53:04 -0400
• Organization: University of Washington, Seattle
• Sender: owner-wri-mathgroup at wolfram.com

```I have needed to perform numerical differentiation as well.  The following
function, which finds the derivative with respect to f[t] at point t0 is
the best I could do.  It gets a little more precision over the regular
definition by defining the derivative slightly differently, and it takes
advantage of Mathematica's arbitrary precision.  I'd love any suggestions
or critique, as this function is actually a cornerstone of some work I'm
_Numerical Recipes in C_

ND[f_, t_, t0_, prec_:\$MachinePrecision] :=
With[{h=1/(2 10^(prec-6)), t0p=SetPrecision[t0,prec]},
N[((f /. t->(t0p+h)) - (f /. t->(t0p=h)))/(2 h), prec]]

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