       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>

```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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