Re: How to cope with tiny numbers in FindRoot

• To: mathgroup at smc.vnet.net
• Subject: [mg63204] Re: How to cope with tiny numbers in FindRoot
• From: "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com>
• Date: Mon, 19 Dec 2005 07:00:57 -0500 (EST)
• Organization: Open University, U.K.
• References: <dnrn37\$pvo\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```<dkjk at bigpond.net.au> a écrit dans le message de news:
dnrn37\$pvo\$1 at smc.vnet.net...
| Hi group,
|
| I'm trying to numerically determine the solution of an equation whose
| coefficients are of the order 10^-100 or less. I've been running into
| all sorts of errors relating to MaxIterations and step size but so far
| I haven't been able to find any useful information in the Mathematica
| book. If you're interested in the notebook i'm using, you can find it
| here:
|
| http://users.bigpond.net.au/jdstokes/theory2.nb
|
| Thanks
|
| James.
|

Hi James,

Having read more carefully your mail and notebook, I may suggest some
options that should help *FindRoot* to deal with small coefficients:

1 - Try not to use the package _RealsOnly_ so Mathematica is free to use the
full range of its internal algorithms (even those that might involve at some
stage use the complex plane).

2 - Enter all the numeric values as exact numbers, 1/2 or 606992/10^5 rather
than 0.5 or 6.06992 for instance.

3 - Use the optional parameters *WorkingPrecision* and *MaxIteration* with
sufficiently high values: I have done some test with 1000 and 500
respectively and got solutions for {omega-ro, 1, 10, 10} and {omega-z, 1,
30, 10}.

Best regards,

/J.M.

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```

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