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Re: Using InterpolateRoot Function in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg41158] Re: [mg41127] Using InterpolateRoot Function in Mathematica
  • From: Bobby Treat <drmajorbob+MathGroup3528 at mailblocks.com>
  • Date: Tue, 6 May 2003 05:58:39 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Needs["NumericalMath`InterpolateRoot`"]
z[L_,x_]=-(2*x*(L*beta-3*deltaY))/L^2-(3*x^2*((-L)*beta+2*deltaY))/L^3;
deltaY=0.000254;L0=.013;alpha=5;
beta=Tan[alpha*(Pi/180)];
f[L_?NumericQ]:=NIntegrate[Sqrt[1+z[L,x]^2],{x,0,L}]-L0
InterpolateRoot[f[L],{L,.01,.02}]

{L -> 0.012992620790646777121996501}

NIntegrate and NumericQ help avoid the messy symbolic integral.  Making 
z an explicit function isn't essential, but I gave up getting past 
NIntegrate's HoldAll attribute without it.

Bobby

-----Original Message-----
From: Haritha Yalamanchili <haritha12 at attbi.com>
To: mathgroup at smc.vnet.net
mathgroup at smc.vnet.net
Subject: [mg41158] Re: [mg41127] Using InterpolateRoot Function in Mathematica

Hi Bobby,

Thank you for the response. I did not enter the exact mathematica 
format, I
only used the symbolic notation to explain the problem (sorry if this 
caused
any confusion). Attached is the mathematica file I was using to solve 
for
the arclength.

deltay, beta and L0 are constants. Also L0 can be used as an initial 
guess
for the root (L).

I was able to solve this problem in Mathcad, on one of my friends 
computer,
but I would prefer to solve in Mathematica , as I am more comfortable 
using
Mathamatica.

Any help that you could provide is greatly appreciated.

Thank You
Prasad
----- Original Message -----
From: "Bobby Treat" <drmajorbob+MathGroup3528 at mailblocks.com>
To: mathgroup at smc.vnet.net
Subject: [mg41158] Re: [mg41127] Using InterpolateRoot Function in Mathematica


> First, why write
>
> f(L) = Integrate[sqrt(1+z^2) dx] - L0 (Integration limits are from 0 
to
> L)
>
> if you mean
>
> f[L_]:= Integrate[sqrt(1+z^2),{z,0,L}] - L0
>
> ??
>
> This leaves me wondering if you entered that, or something else.  The
> possible errors you MIGHT have made are endless, so it would really
> help if you just showed us the statement you entered.
>
> Secondly, what is L0?  Another unknown?  A parameter?
>
> Bobby
>
> -----Original Message-----
> From: Haritha Yalamanchili <haritha12 at attbi.com>
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> Sent: Sun, 4 May 2003 03:56:52 -0400 (EDT)
> Subject: [mg41158] [mg41127] Using InterpolateRoot Function in Mathematica
>
> Hi,
>
> I am trying to use Mathematica to find a value of "L" that satisfies 
the
> equation
>
> Integrate[sqrt(1+z^2) dx] - L0 = 0 (Integration limits are from 0 to 
L)
>
> where,
>
> z= -2 x(L C1 - 3 C2)/L^2 - 3 x^2(-L C1 + 2 C2)/L^3
>
> In order to find the value of L that satisfies the above equation, I
> have
> setup the problem in Mathematica as shown below. Can some one help to
> verify
> if the problem is setup properly of if Mathematica is capable of
> finding a
> root for such functions.
>
> ******
> f(L) = Integrate[sqrt(1+z^2) dx] - L0 (Integration limits are from 0 
to
> L)
>
> InterpolateRoot[ f(L),{L,0,L0} ]
> *******
> (L0=13, C1=0.12, C2=0.25)
>
> Value of L is close to L0 and hence, L0 can be used as the initial 
guess
> value.
>
> Thank You and Best Regards
> Prasad


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