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MathGroup Archive 1999

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RE: Tutorial on NIntegrate needed

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19029] RE: [mg18935] Tutorial on NIntegrate needed
  • From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
  • Date: Tue, 3 Aug 1999 13:44:59 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

L. Dwynn Lafleur wrote:
-----------------------
Anyone know where I might find a tutorial on the art and science of using
NIntegrate efficiently in Mathematica?

===============================

Wolfram Research wrote a tutorial in 1992 and it's available at
http://www.mathsource.com/Content22/General/Tutorials/Numerical/0203-948
Of course some of the info in this tutorial is now obsolete.

However it's a postscript file an you may not have software that can read
it.  If that is the case you can download GhostScript for free.  For the
info on where to get it see 
http://support.wolfram.com/Graphics/Formats/PS/Viewing.html

-------------------------------

I think you will find the tutorial helpful, but nowhere close to covering
the art and science of Numerical Integration.  However, you can experiment
to get an understanding of what some of the options do.  You can use lines
like the ones below to see how the options affect the adaptive algorithm.
Someone with a solid background in numerical integration (I am not
qualified) could make a very good tutorial using examples like those below.


In[16]:=
lst={};
NIntegrate[(lst={lst,x};1/(x-3.95)),{x,4,6},
    MinRecursion->0];
ListPlot[Flatten[lst],PlotJoined->True];

(* Graphic not shown *)


-----------------
In[19]:=
lst={};
NIntegrate[(lst={lst,x};1/(x-3.95)),{x,4,6},
    MinRecursion->2];
ListPlot[Flatten[lst],PlotJoined->True];

(* Graphic not shown *)

--------------------------------

You might also goto 
http://www.mathsource.com/
 Select Publications > Periodical > TheMathematicaJournal > 
        The Mathematica Journal Vol, 5 No 1 --Electronic Supplement

The In-Out discusses a double integral that is best done using symbolic
integration for one integral and numeric integration for other integral.

-----------------------

Regards,
Ted Ersek


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