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Re: Quite Upset with NIntegrate

• To: mathgroup at smc.vnet.net
• Subject: [mg54231] Re: [mg54142] Quite Upset with NIntegrate
• From: Ismail Turan <ituran at bohr.concordia.ca>
• Date: Sun, 13 Feb 2005 22:17:22 -0500 (EST)
• References: <200502110834.DAA09269@smc.vnet.net> <76e8f81805021115033ebef675@mail.gmail.com>
• Sender: owner-wri-mathgroup at wolfram.com

Dear Yehuda,

[Attachments like the Sample.nb below are not permitted.  Contact
the author to obtain it - moderator]

It is kind of hard to show the details here but I am enclosing the
Sample.nb file (hopefully you will get it) including a slightly simplified
integrand (I have much more complicated integrands). When I integrate "in"
with using default options of NIntegrate, I am getting the following data
points :

                 -12            -38
150    9.58287 10    + 1.4816 10    I                         
                -11             -58
152    8.1392 10    + 2.82326 10    I                         
                 -11            -53
154    2.02365 10    + 1.1625 10    I                         
                 -6             -58
156    1.05475 10   + 2.71146 10    I                         
                 -12             -39
158    6.94259 10    + 1.63694 10    I                         
                 -12             -53
160    5.42794 10    + 6.25923 10    I                         
                 -11             -39
162    1.02786 10    + 1.63133 10    I                         
                 -11             -39
164    4.53046 10    + 2.37653 10    I                         
                 -12             -59
166    9.44247 10    + 4.01258 10    I                         
                -11             -40
168    4.8126 10    + 3.48983 10    I                         
                 -10             -40
170    3.71222 10    + 3.94167 10    I   

Here the first column is the varying parameter (mt) and the full range of
it is from 150 to 200 but I only include part of the data points.

The behavior of the curve is certainly expected to increase smoothly as
"mt" increases. Obviously, there is no such pattern here. Setting
MaxPoints something like 500000 (I checked that at least I need to set it
10 times bigger to be sure that data points are accurate enough
but this will increase process time enormously) makes the above values
better looking but still far from being accaptable. So, What is wrong
here?

Thanks,

ismail



On Sat, 12 Feb 2005, yehuda ben-shimol wrote:

> It is difficult to comment without seeing the details. Is there any
> way we can see it?
> yehuda
> 
> On Fri, 11 Feb 2005 03:34:40 -0500 (EST), I. Turan
> <ituran at bohr.concordia.ca> wrote:
> > Hi:
> > 
> > I have been trying to evaluate a 4-dimensional integral by using
> > NIntegrate with Mathematica 4 w2k.  The integrand and even the
> > integration limits are quite complicated (depending on int.
> > variables). The length of the integrand is around 2000 lines in the
> > FortranForm.
> > 
> > If I don't play with any options of NIntegrate, It takes one day to
> > get one data point and gives very  unreasonably weird values. By
> > setting, however, MaxPoints something like 100000 it is possible to
> > get faster results but still it seems that Mathematica couldn't handle
> > it. When I draw a figure from these data points, it appears very very
> > spiky such that it is even not possible to fit the curve. However, it
> > is supposed to be very smooth.
> > 
> > Should I accept that Mathematica can not handle such a
> > numerical integration or is there a way to make Nintegrate working
> > better?
> > 
> > Thanks a lot,
> > 
> > Ismail
> > 
> >
> 

• References:
  • Quite Upset with NIntegrate
    • From: ituran@bohr.concordia.ca (I. Turan)