Using my prev. message code for nint, which will
call quad_qags for this example, I get results which
agree with Mma's pdf tutorial on advanced numerical
integration
(http://www.wolfram.com/learningcenter/tutorialcollection/AdvancedNumericalIntegrationInMathematica/)
for the integrand (p. 2, pdf 5)
(x-2)^2 * sin (4000*x),
over the interval (x,2,3) by using the default epsabs=0.0,
epsrel = 1.0e-8, so only epsrel plays a role, but I get
error no. 1 message from slatec (in all its glory),
------------------------------------------------
(%i29) details:true$
(%i30) nint( (x-2)^2 * sin (4000*x),x,2,3,limit=400);
case quad_qags
***MESSAGE FROM ROUTINE DQAGS IN LIBRARY SLATEC.
***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED
* ABNORMAL RETURN
* ERROR NUMBER = 1
*
***END OF MESSAGE
"too many subintervals done"
est. abs. error = 2.767763E-9
no. of evaluations = 16779
(%o30) -1.586246E-4
-----------------------------------
with the answer the *same* as Mma's answer.
But it I let epsabs be the decider, by setting
epsrel to 0.0, etc, no error message arrives
from slatec, but the answer is not as
accurate.
----------------------------------------------
(%i31) nint( (x-2)^2 * sin (4000*x),x,2,3,epsrel=0.0,epsabs=1e-4,limit=400);
case quad_qags
est. abs. error = 8.183297E-5
no. of evaluations = 10101
(%o31) -1.609751E-4
(%i32) nint( (x-2)^2 * sin (4000*x),x,2,3,epsrel=0.0,epsabs=1e-5,limit=400);
case quad_qags
est. abs. error = 6.045407E-6
no. of evaluations = 10437
(%o32) -1.586189E-4
(%i33) nint( (x-2)^2 * sin (4000*x),x,2,3,epsrel=0.0,epsabs=1e-8,limit=400);
case quad_qags
est. abs. error = 9.961624E-9
no. of evaluations = 14763
(%o33) -1.586246E-4
------------------------------------------------
So, I am wondering if there is some global parameter
which will allow me to turn off the automatic
messages from slatec??
For this type of integral, the epsrel control parameter is
a better choice, but leads to unwanted error messages.
Ted Woollett