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MathGroup Archive 2005

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Re: Numerical integration over half-infinite intervals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60282] Re: Numerical integration over half-infinite intervals
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Sat, 10 Sep 2005 06:46:34 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <dfrgt6$fsg$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

SequenceLimit[list] returns the approximation 
given by Wynn's epsilon \
algorithm to the limit of a sequence whose first 
few terms are given by list. \
Warning: Wynn's epsilon algorithm can give finite 
results for divergent \
sequences.

may help you.

Regards

  Jens

"Alan" <info at optioncity.REMOVETHIS.net> schrieb im 
Newsbeitrag news:dfrgt6$fsg$1 at smc.vnet.net...
|I do a lot of 1D NIntegrates over half-infinite 
domains [0,Infinity).
| Sometimes you can simply put Infinity as an 
upper
| bound and Mathematica will return an answer. In 
that
| case, I don't have a problem.
|
| But, sometimes, this fails or takes too
| long, and I am forced to truncate the integral.
|
| Let's assume my integral converges, is not zero, 
and my
| integrand is relatively smooth with a few 
derivatives, at least.
| Suppose each finite truncated integral can be 
successfully computed to
| the same fixed PrecisionGoal.
|
| Given that, my questions:
|
| Is it possible to extrapolate these truncated 
results to a
| limit with a known precision? If so, how, and 
how does that
| precision relate to the fixed PrecisionGoal 
above?
|
| Thanks,
| alan
|
| 



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