Re: Re: FindRoot cannot find obvious solution

• To: mathgroup at smc.vnet.net
• Subject: [mg47868] Re: [mg47821] Re: FindRoot cannot find obvious solution
• From: Gary.Anderson at frb.gov
• Date: Thu, 29 Apr 2004 03:05:33 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```

the following seems to provide the correct solution.
but, you will get a warning that NIntegrate is having trouble because the
integral is approximately zero.
i think that the code in the original posting may have applied the
Replacement Rule for the y before applying the D function.

exprGen=
Simplify[
With[{h1 = 1 + (yVar - xVar)^2,
h2 = 1 + (2/3 - xVar^2)^2},
With[{b = h2/(h1 + h2),f = xVar(1 - xVar)^2},
expr=(f*D[b, yVar])]]]

g[yArg_?NumberQ]:=
NIntegrate[(expr)/.yVar->yArg,{xVar,0,1}]

FindRoot[g[y] == 0, {y, 0.35, 0.45}]

"Jens-Peer Kuska"
<kuska at informatik.uni-         To:      mathgroup at smc.vnet.net
leipzig-de>                    cc:
Subject: [mg47868] [mg47821] Re: FindRoot cannot find obvious solution
04/28/2004 06:56 AM

Hi,

and what is with

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[yy_?NumericQ] := NIntegrate[Evaluate[s /. y -> yy], {x, 0, 1}]

FindRoot[g[y] == 0, {y, 0.35, 0.45}]

Regards

Jens

"Mukhtar Bekkali" <mbekkali at iastate.edu> schrieb im Newsbeitrag
news:c6l872\$ire\$1 at smc.vnet.net...
> 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
>
>

```

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