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Re: Quite Upset with NIntegrate

• To: mathgroup at smc.vnet.net
• Subject: [mg54357] Re: Quite Upset with NIntegrate
• From: ituran at bohr.concordia.ca
• Date: Sat, 19 Feb 2005 02:32:00 -0500 (EST)
• References: <cv08ak$j42$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi,
My response to Anton appeared before his thread. So, I think it is
better to post my reply again.

Dear Anton,


Thank you for your interest. I am attaching the sample file that has
only
the integrand and the limits even though everything was carried out
with
Mathematica. Below I would like to respond to your questions/remarks
separately.


[contact the author to get the attachment - moderator]



On Tue, 15 Feb 2005, Anton Antonov wrote:
> Dear Ismail Turan,

> As some of the guys in the forum mentioned, it is difficult to answer
your question
> without more detailed information.


> Some questions/remarks:


> 1. From what field this integral comes from?



It is from high energy physics. I am calculating the branching ratio of
a
particle decaying into three particles two of which are off-shell so
that
it doubles my phase space from 2 to 4-dimension.


> 2. How you have entered the integrand in Mathematica? Have you
imported it
>    from, say, a FORTRAN file?


I did everything with Mathematica regardless of the warnings of my
colleagues about the questionable capability of Mathematica in
numerical
integrations(for higher dimensions especially).


> 3. Have you tested are your integrand and boundaries of integration
correctly implemented?


The integrand is checked especially in 2-dimension as a limit of
4-dimensional case and there is a full agreement with the literature
results. The modification coming to the integrand in 4-dimension is to
multipy it by two density functions which reduce to Dirac-Delta
functions
in 2-dimensional limit. In addition to that, the limits in 4-dim are
modified quite simply as far as physics is concerned.


> 4. Using MaxPoints invokes the MonteCarlo method.
>    You might try QuasiMonteCarlo method -- it is as fast as
MonteCarlo,
>    and has more deterministic nature.


I tried what you have suggested here and I got the same data points
when I
set MaxPoints to somevalue but  leave the "Method" option "Automatic".


> 5. The default option settings in NIntegrate invoke the
MultiDimensional integration method.
>    You might try using a Cartesian rule method with
Method->GaussKronrod.


This made the process very slow. I haven't been able to get one data
point
so far (within aproximately five hours).

Thank you very much again. I really appreciate all the help.


Best Regards,