BesselK problems at large argument?
- To: mathgroup at smc.vnet.net
- Subject: [mg78860] BesselK problems at large argument?
- From: AES <siegman at stanford.edu>
- Date: Wed, 11 Jul 2007 06:14:37 -0400 (EDT)
- Organization: Stanford University
Optical fiber mode calculations, at least if done programmed
straightforwardly, require evaluating integrals of r BesselK[0, w r]^2
and r^3 BesselK[0, w r]^2 from a finite value r = a out to r = infinity,
for smallish (order unity) values of w and a , using NIntegrate and with
all quantities real.
Trying to do this for different parameter values, however, I keep
running into messages saying things like "Integral failed to converge to
desired precision," or at other times
BesselK[0, r] is not numerical at {r} = {5.`*^8}
I don't think there's a programming error involved, because for some
values of the parameters everything comes out just fine.
I'm aware that BesselK[ ] has a simple asymptotic form at large r , and
I suppose I could mess around trying to switch to it at large r , or
figure out some way to truncate the integral at some large outer limit.
But, hey, BesselK is a nice smooth, non-oscillatory (and long known)
function, which decreases very rapidly at large r. Shouldn't these
integrals work OK -- or more important, is there an option I can set to
make them go OK?
[This is still 5.2 on Mac OS 10.3.9.]