Re: NIntegrate of a Decaying Exponential
- To: mathgroup at smc.vnet.net
- Subject: [mg15171] Re: [mg15137] NIntegrate of a Decaying Exponential
- From: BobHanlon at aol.com
- Date: Thu, 17 Dec 1998 00:27:49 -0500
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 12/16/98 8:44:51 AM, arc at astro.columbia.edu writes:
>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!
>
AC,
$Version
Power Macintosh 3.0 (May 6, 1997)
I do not get the error message.
NIntegrate[-2 v Exp[-v^2], {v, -1, 2}]
-0.349564
However, why are you using numerical integration? This function can be
integrated.
Integrate[-2 v Exp[-v^2], {v, -1, 2}]
E^(-4) - E^(-1)
% // N
-0.349564
Integrate[-2 v Exp[-v^2], {v, -1., 2}]
-0.349564
Bob Hanlon