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Re: Quite Upset with NIntegrate

• To: mathgroup at smc.vnet.net
• Subject: [mg54275] Re: Quite Upset with NIntegrate
• From: Ismail Turan <ituran at bohr.concordia.ca>
• Date: Wed, 16 Feb 2005 14:35:55 -0500 (EST)
• References: <42120FED.60501@wolfram.com>
• Sender: owner-wri-mathgroup at wolfram.com

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,