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Re: Using FindRoot or interpolation function with symbolic argument

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92187] Re: Using FindRoot or interpolation function with symbolic argument
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Mon, 22 Sep 2008 07:09:43 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <gb7ob8$nfp$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

a) the Compile[] is pure nonsense, what should be faster when calling
    the FindRoot[] function.
b) you mean
      f[y_?NumericQ] := x /. FindRoot[ArcTanh[x] == y x, {x, 99/100}]

c) your final question "Is there a way to define an NDSolve-digestible 
equation that calls FindRoot with symbolic arguments?" is just the 
opposite of that what you like to do ..

Regards
   Jens

exoptery at gmail.com wrote:
>      I'd like to use NDSolve to integrate a pair of ODEs.  Expressing
> the system as a set of explicit equations, however, requires the
> inverse of ArcTanh[x] / x.  I thought I'd define a function for this
> as follows:
> 
> 
>      f = Compile[{{y, _Real}}, x /. FindRoot[ArcTanh[x] == y x, {x,
> 99/100}]];
> 
> 
> However, when I set, say,
> 
> 
>       eqn1 = u'[R] == u[R] f[(u[R] (1 + v[R])^2)/(1 + v[R]^2)]
> 
> 
> Mathematica clearly dislikes the use of symbols instead of a numerical
> argument.
> 
> 
>      Is there a way to define an NDSolve-digestible equation that
> calls FindRoot with symbolic arguments?
> 
>      Thank you for your attention.
> 
>      J.
> 


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