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Re: a bug in mathematica 5?

• To: mathgroup at smc.vnet.net
• Subject: [mg43212] Re: a bug in mathematica 5?
• From: "Alan" <infoNOSPAM at optioncity.net>
• Date: Tue, 19 Aug 2003 07:53:15 -0400 (EDT)
• References: <bh2714$hra$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

"Li-Xin Li" <lli at fas.harvard.edu> wrote in message
news:bh2714$hra$1 at smc.vnet.net...
> Is the following a bug in mathematica 5?
>
> I typed
> sol[x_] := NDSolve[{y'[t] == x Sin[t] y[t], y[0.01] == 1},
>                    y, {t, 0.01, 10}]
> u[x_] := ((y[1] /. sol[x])[[1]]) - 3
>
> to define a function u[x]. It works, e.g. u[1] = -1.41648.
>
> Then, I typed
> FindRoot[u[x] == 0, {x, 2, 3}]
> to find the root for u[x] = 0. But this does not work. Instead, it
> gives the following error messages:
>
> NDSolve::ndnum: Encountered non-numerical value for a derivative at
>         t==0.01`.
> ReplaceAll::reps: {NDSolve[{y'[t] == x Sin[t] y[t], y[0.01] == 1},
>         y, {t, 0.01, 10}]} is neither a list of replacement rules nor
>         a valid dispatch table, and so cannot be used for replacing.
> FindRoot::ndnum: The function value {-3+y[1.]} is not a list of
>         numbers with dimension {1} at {x} = {2.}.
>
> This small program works perfectly for 4.1 and 4.2, but not for
> 5. Does anybody knows why?
>
> If it is really a bug, how to inform the wolfram company?
>
> Best wishes,
> Li-Xin Li

I am also seeing what seems to me to be a bad bug in the 5.0 FindRoot
function. As far as I can tell, the problem occurs when you attempt to
execute
FindRoot[ f [x] == 0, {x, x0, x1}] for a "sufficiently complicated" f[x].
The bug
seems to be that the routine "sometimes" just passes a symbolic 'x' to f[x]
instead of a numerical value.
Whether or not you get this bug seems to depend upon what f[x] actually
does.

In my case, f[x] was a Module with a numerical integration embedded, which
of
course then failed because the integrand was not numeric. When I then
inserted a Print[x]
at the top of the f[x_] Module, I got an 'x' and not a number! This renders
the FindRoot function useless,
of course, unless someone sees a work-around.

This problem was spotted by good code that executes fine in 4.1 but fails
badly in 5.0.
(I did have to change {x, {x0 , x1}} to {x, x0, x1}, as per
the Help Browser. The Help Bowser doc changes definitely suggest that this
this function has been modified.

Any comments from others who have seen this, or see a work-around, or
WRI people would be most appreciated.

Regards,
alan

• Follow-Ups:
  • Re: a bug in mathematica 5?
    • From: Jason Sidabras <sidabras.jason@nsgcorp.net>