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Re: [Help-gsl] Numerical integration

From: Inigo Aldazabal Mensa
Subject: Re: [Help-gsl] Numerical integration
Date: Thu, 3 Sep 2009 13:21:38 +0200
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El Miércoles, 2 de Septiembre de 2009, Jonny Taylor escribió:
> Hi all,
> My code needs to numerically integrate a function between known finite
> limits (which is what currently takes most of its run time), and I am
> trying to work out of any of the GSL routines can help with this. The
> function has a sort of carrier/envelope form:
> f(x) = g(x) exp(i a x)
> and I am trying to determine:
> int(f(x), 0, x2)

You can try w

> g(x) is a function which has a known, fairly complicated, but well-
> behaved, analytical form (and it doesn't appear possible to even begin
> to symbolically integrate either f(x) or g(c))
> At the moment I am just using a simple Simpson's rule to integrate it.
> The carrier frequency is not enormous, but is high enough frequency to
> require quite a few sample points. I feel that because of this
> specific form there ought to be some sort of shortcut or special
> technique that could separate out the "carrier wave", so that
> effectively all that needs to be sampled is the slowly-varying
> envelope. Can anyone suggest a suitable technique that I could use for
> this? (ideally one implemented in GSL, but I can code it up from
> scratch if required). Someone suggested to me that some sort of trick
> involving fourier transforms might help, but I haven't really got
> anywhere with that as yet.
> Thanks in advance for any suggestions
> Jonny
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