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Re: Finding derivatives of a list?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg40840] Re: [mg40816] Finding derivatives of a list?
  • From: Selwyn Hollis <selwynh at earthlink.net>
  • Date: Mon, 21 Apr 2003 06:59:04 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

The "usual" second-order accurate formula,

(y[[i+1]] - 2 y[[i]] + y[[i-1]])/h^2,

is easy to apply with ListCorrelate. For example:

h=.1; vals = Table[Sin[x], {x, 0, 1, h}]

      {0, 0.0998334, 0.198669, 0.29552, 0.389418, 0.479426,
         0.564642, 0.644218, 0.717356, 0.783327, 0.841471}

ListCorrelate[{1, -2, 1}/h^2, vals]

      {-0.0997502, -0.198504, -0.295274, -0.389094, -0.479026,
       -0.564172, -0.643681, -0.716758, -0.782674}

-----
Selwyn Hollis
http://www.math.armstrong.edu/faculty/hollis

On Saturday, April 19, 2003, at 11:02  PM, AES/newspost wrote:

> Specific problem is how to generate a list of values of the second
> derivative of a relatively smooth function at a set of equally spaced
> points, when the function itself is known only as a list of numerical
> values at those same points?
>
> -- 
> "Power tends to corrupt.  Absolute power corrupts absolutely."
> Lord Acton (1834-1902)
> "Dependence on advertising tends to corrupt.  Total dependence on
> advertising  corrupts totally." (today's equivalent)
>



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