- To: mathgroup at smc.vnet.net
- Subject: [mg35496] Integration problem
- From: Arnold Gregory Civ AFRL/SNAT <Gregory.Arnold at wpafb.af.mil>
- Date: Tue, 16 Jul 2002 04:50:05 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On Mathematica 4.1 w/ Win2000, I'm having the following problem with an integral:
In:= expr1 = (t)^2* UnitStep[1 - t^2 - 81. t^4]
Out= t^2 UnitStep[1 - t^2 - 81. t^4]
In:= expr2 = (0.+ t)^2 UnitStep[1 - t^2 - 81. * t^4]
Out= (0.+ t)^2 UnitStep[1 - t^2 - 81. * t^4]
Out= (10*Sqrt[26*(-1 + 5*Sqrt)] -
2*Sqrt[-2 + 10*Sqrt])/8748
NIntegrate::slwcon: Numerical integration converging too slowly; suspect one \
of the following: singularity, value of the integration being 0, oscillatory \
integrand, or insufficient WorkingPrecision. If your integrand is oscillatory \
try using the option Method->Oscillatory in NIntegrate.
NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after \
7 recursive bisections in t near t = -0.320313.
It doesn't matter if I put the expression directly into the integrals. I can remove the difference by rationalizing either the expression t+0. or UnitStep[...] & both cases give the correct result. I can also change to (t+eps) and then evaluate eps->0. and get the correct result. In short, it looks like this particular form yields an unstable result & I'm looking for advice on approaches to mitigate this happening within a sequence of long & complex calculations. It isn't clear to me that Rationalize is the best approach or that it will always guarantee correcting the problem.
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