Re: NIntegrate of a Decaying Exponential

• To: mathgroup at smc.vnet.net
• Subject: [mg15172] Re: [mg15137] NIntegrate of a Decaying Exponential
• From: Jurgen Tischer <jtischer at col2.telecom.com.co>
• Date: Thu, 17 Dec 1998 00:27:49 -0500
• Organization: Universidad del Valle
• References: <199812160811.DAA24490@smc.vnet.net.>
• Sender: owner-wri-mathgroup at wolfram.com

Wretch,
nomen est omen. Try Integrate[-2 v Exp[-v^2],v] --- or a beginner's
calculus book.

Jurgen

Wretch wrote:
>
> 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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