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