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[Help-gsl] Integration advice


From: Jonny Taylor
Subject: [Help-gsl] Integration advice
Date: Thu, 12 Jun 2008 14:24:50 +0100

Hi all,

I'm hoping somebody may be able to advise me on a numerical integration problem I have. This may be as much a maths question as a GSL question, but I'd appreciate any input people can offer.

I have an integral over a variable t, an integral involving two other constants r and z. The integral will be evaluated many, many times for different r, z, but over the same range 0 to 1 every time. i.e. the integral has the form:

Int_0^1 { f(r, z, t) g(t) dt }

f(r, z, t) is a relatively simple (though highly oscillatory) function involving an exponential and a Bessel function. g(t) is a nasty mix of trig and Legendre functions.

Assuming the integral can't be solved analytically (I'm pretty sure _I_ can't solve it, at least!), I'm trying to work out the fastest way of numerically integrating the function. What I am hoping is that there is some clever trick (hopefully implemented in gsl...) that will allow me to do the hard work once at the start, and then be able to repeatedly evaluate the integral for different r, z relatively quickly. I feel that because the integral is "separable" into f(r, z, t) and g(t) then there may be some way of speeding up the computation. I have no idea what that method might be though.

Any advice would be greatly appreciated...

Jonny




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