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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
- [Help-gsl] Integration advice,
Jonny Taylor <=