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MathGroup Archive 1998

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NIntegrate of a Decaying Exponential

  • To: mathgroup at smc.vnet.net
  • Subject: [mg15137] NIntegrate of a Decaying Exponential
  • From: Wretch <arc at astro.columbia.edu>
  • Date: Wed, 16 Dec 1998 03:11:13 -0500
  • Organization: Vacuum
  • Sender: owner-wri-mathgroup at wolfram.com

Greetings -- I'm trying to get Mathematica to do an integral that
appears regularly in plasma physics problems.  It appears to give the
right answer, but it's always accompanied with an annoying error
message whose roots are a bit vague.  Here is the function to be
integrated:

f = -2 v Exp[-v^2]  over the v-interval  (-1,2)

The answer should be about  -.34956 (according to an IMSL subroutine)

Here's the mathematica input and output:

In[1]:=NIntegrate[-2 v Exp[-v^2],{v,-1,2}] Out[1]:=Out[99]=-0.349564

NIntegrate::"ploss": 
    "Numerical integration stopping due to loss of precision. Achieved \
neither the requested PrecisionGoal nor AccuracyGoal; suspect highly \
oscillatory integrand, or the true value of the integral is 0. If your
\ integrand is oscillatory try using the option Method->Oscillatory in
\ NIntegrate."

So, Mathematica gets it right, but with the mysterious warning. The
error/warning message isn't surprising since the integrand has such a
sharp peak at v=0, but none of the options specified in the help menu,
such as MinRecursion, MaxRecursion, Method->, etc. were of any use in
suppressing this error message.  I want to suppress messages of this
sort not only so that I don't have to look at them, but also to have an
extra measure of confidence that the answer is actually right!  

Any help is greatly appreciated.

Thanks,

AC


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