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I'm trying to take an integral of a super oscillatory function as follows. It takes a long time to solve it with the NIntegrate so I added the option Method -> {Automatic, "SymbolicProcessing" -> 0}. It's absolutely faster but the answers are completely different.

Can anyone tell me what is wrong with the options please? Is there any way to take an integral of super oscillatory functions in Mathematica?

In addition, the original integral's results without the option seem kind of weird because they are oscillating between large positive values and large negative values.

I have attached my code:

NIntegrate[
  (Exp[(k/(2*Pi))*
    (-a*Abs[r*Cos[t] - rprime*Cos[tprime]] -b*Abs[r*Sin[t] - rprime*Sin[tprime]])])*
      Cos[k*Abs[r*Cos[t]-rprime*Cos[tprime]]]*r*rprime, 
  {r, 0,Infinity}, {t, 0, 2*Pi}, {rprime, 0, Infinity}, {tprime, 0, 2*Pi}]
Improve this question
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    $\begingroup$ Since you are using NIntegrate, what are the values for a, b, and k? $\endgroup$
    – Bob Hanlon
    Commented Sep 29, 2016 at 0:15
  • $\begingroup$ a=3.2, b=7 and k can be a value between 0.1 to infinity, actually I want to compare the results for different value of k. $\endgroup$
    – Mohammad
    Commented Sep 29, 2016 at 14:49

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