Re: Message: "Numerical interation converging too slowly"

• To: mathgroup at smc.vnet.net
• Subject: [mg83263] Re: Message: "Numerical interation converging too slowly"
• From: "Hoa Bui" <hoabui05 at gmail.com>
• Date: Fri, 16 Nov 2007 05:33:17 -0500 (EST)
• References: <fhh7h5\$8p4\$1@smc.vnet.net> <473C8ACF.80000@gmail.com>

```Thanks, Jean-Marc!
Yes, I am using Mathematica 5.2 and I did get the same graph except
that it goes along with the message previously mentioned.

Also, check this out:

It is okay to integrate from the first to the last point:
In[89]:=NIntegrate[linN[s],{s,lstã??1,1ã??,lstã??4,1ã??}]
Out[89]=0.00978246

But if I do the same with a different set of points:
lst2 = {{0, 0}, {0.005117241776887967`, 0.12109827984374989`}, \
{0.015699480276911173`, 0.159661398624297`}, {0.04816533822543266`, \
0.2770434111412446`}}
In[91]:=lin=Interpolation[lst2,InterpolationOrder\[Rule]1];
In[92]:=NIntegrate[lin[s],{s,lst2ã??1,1ã??,lst2ã??4,1ã??}]
I get another weird message:
"NIntegrate::ncvb : NIntegrate failed to converge to prescribed
accuracy after 7 recursive bisections in s near s =
0.005079938015963601`. More... "
Out[92]=0.00888437

I have no idea what's going on here! Please help!
Thanks,
HB

On 11/15/07, Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com> wrote:
> Hoa Bui wrote:
> > Hi all,
> >
> > Please help!
> >
> > I have a list of points:
> > lst={{0,0.0673209172484956`},{0.003449278068524249`,0.10109827933089396`},{\
> > 0.014031516572727063`,0.19966139796005267`},{0.04649737451028208`,0.\
> > 2870434103185859`}}
> >
> > I then define a function NN[x] that returns the linearly interpolated
> > value at x:
> > linN = Interpolation[lst, InterpolationOrder -> 1];
> > NN[x_?NumberQ]:=linN[x];
> >
> > In[17]:=NN[0]
> > Out[17]=0.0673209
> >
> > In[18]:=NIntegrate[NN[s],{s,0,0.45}]
> > Out[18]=0.344713
> >
> > However, if I want to make the integral a function of the upper limit,
> > and plot it:
> > Plot[NIntegrate[NN[s],{s,0,z}],{z,0,0.045}],
> > I get this message:
> > "NIntegrate::slwcon: Numerical integration converging too slowly; suspect one \
> > of the following: singularity, value of the integration being 0, oscillatory \
> > integrand, or insufficient WorkingPrecision. If your integrand is oscillatory \
> > try using the option Method->Oscillatory in NIntegrate."
> >
> > Maybe there's nothing wrong with the result, but I'm not sure. And the
> > message is annoying, too.
> > Does anyone know how to make Mathematica do the work without complaining?
> >
> > I appreciate it.
> > HB
> >
>
> Hum, the posted code works fine (i.e. no warning nor error messages are
> issued) with Mathematica 6.0.1. I have uploaded the following pdf on my
> web site so you can check the graph produced by your version against
> version 6:
>
> http://homepages.nyu.edu/~jmg336/mathematica/HoaBuiIntegration.pdf
>
> (Sorry, I am away from my machine with version 5.2 installed, so I
> cannot investigate further.)
>
> Regards,
> --
> Jean-Marc
>

```

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