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MathGroup Archive 1998

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Re: NIntegrate of a Decaying Exponential

  • To: mathgroup at smc.vnet.net
  • Subject: [mg15180] Re: NIntegrate of a Decaying Exponential
  • From: "Allan Hayes" <hay at haystack.demon.co.uk>
  • Date: Fri, 18 Dec 1998 02:10:57 -0500
  • References: <75a179$rv3@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Wretch wrote in message <75a179$rv3 at smc.vnet.net>...
........
>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!
.........

Hi,

Messages are turned off and on in this way

Off[NIntegrate::"ploss"]

On[NIntegrate::"ploss"]

However I don't get the message that you report:

With
$Version
"Microsoft Windows 3.0 (April 25, 1997)"


NIntegrate[-2 v Exp[-v^2],{v,-1,2}]

    -0.349564

In fact the integral can be computed sybolically a

Integrate[-2 v Exp[-v^2],{v,-1,2}]

    1/E^4 - 1/E

N[%]

    -0.349564

However, I get the message if I set the PrecisionGoal high enough.

NIntegrate[-2 v Exp[-v^2],{v,-1,2}, PrecisionGoal->16]
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."

    -0.349564

Now turn off the message

Off[NIntegrate::"ploss"]

Check:

NIntegrate[-2 v Exp[-v^2],{v,-1,2}, PrecisionGoal->16]

    -0.349564

And turned back

On[NIntegrate::"ploss"]

Allan

---------------------
Allan Hayes
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565





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