Re: Re: Message: "Numerical interation converging too slowly"

*To*: mathgroup at smc.vnet.net*Subject*: [mg83311] Re: [mg83263] Re: Message: "Numerical interation converging too slowly"*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Sat, 17 Nov 2007 05:23:05 -0500 (EST)*References*: <fhh7h5$8p4$1@smc.vnet.net> <473C8ACF.80000@gmail.com> <5270064.1195230612282.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

Version 6.0.1 has no problem with this, but for either version I'd suggest a different approach: lst = {{0, 0.0673209172484956`}, {0.003449278068524249`, 0.10109827933089396`}, {0.014031516572727063`, 0.19966139796005267`}, {0.04649737451028208`, 0.2870434103185859`}}; {lo, hi} = lst[[{1, -1}, 1]]; linN = Interpolation[lst, InterpolationOrder -> 1]; Clear[integral] integral = integral /. First@NDSolve[{integral'[s] == linN[s], integral[lo] == 0}, integral, {s, lo, hi}]; Plot[integral[z], {z, 0, 0.045}] Bobby On Fri, 16 Nov 2007 04:33:17 -0600, Hoa Bui <hoabui05 at gmail.com> wrote: > > 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£â?¬Å¡1,1Ã£â?¬â?º,lstÃ£â?¬Å¡4,1Ã£â?¬â?º}] > 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£â?¬Å¡1,1Ã£â?¬â?º,lst2Ã£â?¬Å¡4,1Ã£â?¬â?º}] > 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 >> > > -- DrMajorBob at bigfoot.com