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MathGroup Archive 1996

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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 
doing.  There's more info on numerical differentiation in the book 
_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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Russell D. Brunelle             |  Lab Ph.:  (206) 685-4343
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