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