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Topic: highly accurate pde solvers?
Replies: 6   Last Post: Nov 30, 2012 5:34 AM

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Leslaw Bieniasz

Posts: 171
Registered: 12/13/04
Re: highly accurate pde solvers?
Posted: Nov 30, 2012 5:09 AM
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On Fri, 30 Nov 2012, Rui Maciel wrote:

> I don't know of free programs, but I believe Mathematica does support
> arbitrary precision numbers.


I have tried MATHEMATICA, but my general impression is that
the error control is entirely unreliable. Even if one requests
AccuracyGoal->12 and PrecisionGoal->12, the program returns
at most 3-4 accurate digits. Requesting higher precision produces
failures due to the lack of memory, etc.
The above is probably easy to predict, since MATHEMATICA seems
to use rather standard non-adaptive finite-differences, and these usually
cannot be more accurate. So, it seems that the arbitrary precision
arithmetic is not really of advantage in MATHEMATICA, at least
in the case of the PDE solving.

(or maybe I am wrong and someone will tell me how to overcome these
barriers).

Leslaw



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