[Help-gsl] Numerical integration

[Jonny Taylor]

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)

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