Re: FindRoot cannot find obvious solution

*To*: mathgroup at smc.vnet.net*Subject*: [mg47828] Re: [mg47806] FindRoot cannot find obvious solution*From*: Anton Antonov <antonov at wolfram.com>*Date*: Thu, 29 Apr 2004 00:33:44 -0400 (EDT)*References*: <200404270847.EAA18892@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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 > > > You can try this: In[158]:= Clear[f, g, s, y, x] 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[s_, (y_)?NumericQ] := NIntegrate[s, {x, 0, 1}]; FindRoot[g[s, y] == 0, {y, 0.35, 0.45}] Out[165]= {y -> 0.3993706824894056} The reason why NIntegrate gives "inum"messages is explained at http://support.wolfram.com/mathematica/mathematics/numerics/nsumerror.html Anton Antonov Wolfram Research, Inc.

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