Hi, I am trying to compute this integral for different a
with 0.0001<a<0.5
,
int[a_?NumericQ, r_?NumericQ]:=NIntegrate[Exp[-a/Sqrt[1-x^2]]/(x^2-r^2)^2, {x, 0, r, 1},Method ->"PrincipalValue"]
where 0<r<1
. For high a
, the calculation don't display errors,
int[100, 0.8]
(* 1.1619041*10^-44 *)
But for a={0.1,0.01,0.0001}
I get this message error.
int[0.1, 0.8]
NIntegrate::inumri: The integrand E^(-(0.1/Sqrt[1-Power[<<2>>]]))/(-0.64+(0.8 -x)^2)^2+E^(-(0.1/Sqrt[1-Power[<<2>>]]))/(-0.64+(0.8 +x)^2)^2 has evaluated to Overflow, Indeterminate, or Infinity for all sampling points in the region with boundaries {{0.,2.7247563*10^-30}}.
I still can't control the accuracy of the calculation. I proceeded by increasing WorkingPrecision
, PrecisionGoal
, MaxRecursion
but it gives each time different values, I do not even know if it gives the true value.
Please, how to increase the precision of this computation?
Problem not solved yet on stackexchange.