Precision available with NIntegrate {Method -> Oscillatory}

*To*: mathgroup at smc.vnet.net*Subject*: [mg74038] Precision available with NIntegrate {Method -> Oscillatory}*From*: "Peter" <petersamsimon2 at hotmail.com>*Date*: Wed, 7 Mar 2007 03:10:52 -0500 (EST)

Hi. I'm helping someone with a scientific programming problem, and I wanted to get a high accuracy result to use as a reference solution. I am able to get 15 digits of accuracy for a non-oscillatory integral, but it appears that when I specify the option Method -> Oscillatory for NIntegrate, it ignores my precision request: -------------------------------------------------------------------- a = 0; b = 6706902 * 10^\(-7); c = 589300 * 10^(-6); d = 9802874 * 10^(-7); t = -5026548 * 10^(-6); =CE=B1 = 0; Iint = NIntegrate[(b^2 - 2 d Cos[t + x] b + d^2 + (a + b c x)^2)^(-3/2), {x, =CE=B1, Infinity}, {PrecisionGoal -> 15, WorkingPrecision -> 30, MaxRecursion -> 200}] 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. More... 1=2E46869038002327 Cint = NIntegrate[Cos[x]/(b^2 - 2 d Cos[t + x] b + d^2 + (a + b c x)^2)^(3/2), {x, =CE=B1, Infinity}, {PrecisionGoal -> 15, WorkingPrecision - > 25, MaxRecursion -> 300, Method -> Oscillatory}] 0=2E2592156 -------------------------------------------------------------------- I'm not concerned about the slow convergence warning on the first integral, Iint. Rather, the second integral, Cint, is only evaluated to a precision of 8 digits, despite the explicit request for more in the call to Nintegrate. Does anyone have a suggestion to obtain 15 digits of precision on the second integral? Thanks, Peter