Re: FindRoot cannot find obvious solution

*To*: mathgroup at smc.vnet.net*Subject*: [mg47827] Re: [mg47806] FindRoot cannot find obvious solution*From*: Oleksandr Pavlyk <pavlyk at phys.psu.edu>*Date*: Wed, 28 Apr 2004 06:56:20 -0400 (EDT)*Organization*: Penn State University; Department of Physics*References*: <200404270847.EAA18892@smc.vnet.net>*Reply-to*: pavlyk at phys.psu.edu*Sender*: owner-wri-mathgroup at wolfram.com

Hi Mukhtar, Attributes[NIntegrate] {HoldAll, Protected} So s is not evaluated until later. Your code would look much cleaner if you kept arguments of your functions explicitly h1[x_, y_] = 1 + (y - x)^2; h2[x_] = 1 + (2/3 - x^2)^2; b[x_, y_] = h2[x]/(h1[x, y] + h2[x]); s[x_, y_] = FullSimplify[ x*(1 - x)^2*Evaluate[ D[b[x, y], y]]]; g[y_] := NIntegrate[s[x, y], {x, 0, 1}] Now, unlike in your code, Plot[g[y],{y,0.2, 0.8}] does plotting without prolifirating bunch of errors. Furhermore, it produces correct result for FindRoot: FindRoot[g[y], {y, 0.35, 0.45}, WorkingPrecision -> 16] << Error messages NItegrate::ploss suppressed >> {y -> 0.399370682489405571438\ 7173794`16.} If those messages annoy you, like they do for me, you can work with the interpolated function ig = Interpolation[ Table[{y, g[y]}, {y, 0.2, 0.8, 0.005}], InterpolationOrder -> 5]; Then the result is spit out without errors. FindRoot[ig[y], {y, 0.35, 0.45}, WorkingPrecision -> 16] {y -> 0.399370682489405632471\ 6472443`16.} So now I've got the question for the group. It seems to me like a general problem, having a function f[x], defined via Integral (or Sum, or Product) f[x] = Integrate[ f[x,y],{ y, domain}] i can plot the function, and see it's zero approximately, but when fed to FindRoot, I get a bunch of errors. I do not understand why, but that aside, the only clean way out is to interpolate f[x] first, and then use FindRoot. If anybody on the list has a better workaround, please share :). Your insight would be greatly appreciated. Regards, Sasha Mukhtar Bekkali wrote: > Here is my code in Mathematica 5: > > h1=1+(y-x)^2; > h2=1+(2/3-x^2)^2; > b=h2/(h1+h2); > f=x(1-x)^2; > s=f*D[b,y]; > g[y_]:=NIntegrate[s,{x,0,1}]; > FindRoot[g[y]==0,{y,0.35,0.45}] > > The output is > > NIntegrate::inum: Integrand H is not numerical at {x} = {0.5`}. > FindRoot::cvmit: Failed to converge to the requested accuracy or precision > within 100 iteration > > and it gives me y->0.45 or the upper boundary. However, when I plot g[y] I > can see that the solution is somewhere around y=0.4. Using Solve instead of > FindRoot does not give me any solutions. > > What am I doing wrong here? Thank you in advance. Mukhtar Bekkali

**References**:**FindRoot cannot find obvious solution***From:*"Mukhtar Bekkali" <mbekkali@iastate.edu>