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Re: Q: Approximation of derivative

• To: mathgroup at smc.vnet.net
• Subject: [mg26360] Re: Q: Approximation of derivative
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 13 Dec 2000 02:41:20 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <90v65b$711@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

any derivative of a Lagrange interpolation
with more than 2 points will give you a new
approximation to the derivative. The most
accurate variant is to use Richardson-Extrapolation
as describet in

http://lib-www.lanl.gov/numerical/bookcpdf/c5-7.pdf

Better as yours are

(f(x+h)-f(x-h))/(2h)

For a five point formula you can just type

ip = InterpolatingPolynomial[{{x, f}, {x + h, f1}, {x + 2h, f2}, {x +
3h, 
          f3}, {x + 4h, f4}}, t];

FullSimplify[D[ip, t] /. t -> x + 2h]

Hope that helps
  Jens

Elias Kyriakides wrote:
> 
> Dear friends,
> 
> I was wondering whether there exists a better approximation of the
> derivative of a function besides the known (f(x+Dt)-f(x))/Dt
> 
> I would be grateful if somebody told me what it is or where i could find
> it.
> 
> Thank you in advance,
> Elias