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MathGroup Archive 2005

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Re: Re: NSolve Vs. Elliptic Integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62532] Re: [mg62500] Re: [mg62471] NSolve Vs. Elliptic Integral
  • From: Pratik Desai <pdesai1 at umbc.edu>
  • Date: Sun, 27 Nov 2005 02:40:09 -0500 (EST)
  • References: <200511260746.CAA06410@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Bob Hanlon wrote:

>NSolve is intended primarily for polynomials (see Help browser).  Use 
>FindRoot.
>
>Clear[f,g];
>
>f[x_,m_]:=Sqrt[(1+0.176*Sin[m]^2*Sin[x]^2)*
>        (1+1.018*Sin[m]^2*Sin[x]^2)/(1-Sin[m]^2*Sin[x]^2)];
>
>g[m_]:=0.159*Sqrt[1/(-9*10^(-6)+Sin[m]^2)];
>
>FindRoot[
>  NIntegrate[f[x,m],{x,ArcSin[0.003/Sin[m]],Pi/2}]==g[m],
>  {m,1}]
>
>{m -> 0.102762168294469}
>
>Plot[{NIntegrate[f[x,m],{x,ArcSin[0.003/Sin[m]],Pi/2}],g[m]},
>    {m,0.05,.15},PlotStyle->{Blue,Red},Frame->True,Axes->False];
>
>
>Bob Hanlon
>
>  
>
>>From: "nilaakash at gmail.com" <nilaakash at gmail.com>
To: mathgroup at smc.vnet.net
>>    
>
>>Date: 2005/11/25 Fri AM 02:25:24 EST
>>Subject: [mg62532] [mg62500] [mg62471] NSolve Vs. Elliptic Integral
>>
>>Dear Friends,
>>                       I am facing a problem to NSolve an  Elliptic
>>Integral like that.
>>
>>f[x_] := Sqrt[(1 +
>>          0.176*Sin[m]^2*Sin[x]^2)*(1 + 1.018*Sin[m]^2*Sin[x]^2)/(1 -
>>            Sin[m]^2*Sin[x]^2)]
>>
>>g[m] = 0.159*Sqrt[1/(-9*10^(-6) + Sin[m]^2)];
>>
>>NSolve[NIntegrate[f[x], {x, ArcSin[0.003/Sin[m]], Pi/2}] == g[m], m]
>>
>>
>>Here I want to get an "m" value such that integration value = g[m].
>>
>>This NSolve shows problem, please could any body tell me how to get
>>exact m value.
>>
>>Thanks.
>>
>>nilaakash
>>
>>
>>    
>>
>
>  
>
Hi Bob,

What version of Mathematica are you using?
Because it gives me the result you reported but when I tried to just do 
the NIntegrate it does not evaluate. Maybe I am missing something??
Is this a functionality of find root  (if that is true, that is pretty 
interesting) or something else

Please advise

Pratik

-- 
Pratik Desai
Graduate Student
UMBC
Department of Mechanical Engineering
Phone: 410 455 8134



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