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numerical capabilities

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68260] numerical capabilities
  • From: dimmechan at yahoo.com
  • Date: Mon, 31 Jul 2006 03:45:13 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

 Hi to all.

I work as a researcher in an engineering university and recently I
was asked to demonstrate the numerical capabilities of Mathematica to
 some collegues and professors. I have prepared a presentation based
on my experience, Mathematica book, Gass' book for Mathematica,
material
 from this forum and some articles/notebooks regarding numerical
computation I have found in Wolfram's site.

 Already I have a lot of staff as regards the numerical solution of
 differential and algebraic equations and the numerical evaluation of
 integrals.

However, what I really need is to establish my belief that the
results obtained by the used numerical built-in functions (for example
NIntegrate) are the same reliable, if not more than those obtained
from other systems.

Here in the university, I have a lot of arguments with people who
believe that for numerical integration (e.g. for improper very slowly
convergent oscillatory integrals) or for
more advanced numerical computations (e.g. in Finite and Boundary
Ellements) is better to use other systems or programming languages.

 I have found a lot of examples of complicated integrals (proper and
improper) that Mathematica evaluated accurately, but still I can
convince them that the numerical integration offers reliability,
speed and insight.

Any ideas will be greatly appreciated.
 
Thanks in advance.


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