I am trying to solve an integral using NIntegrate:

NIntegrate[ (u/(u^2 + v^2))*r*x*Exp[-2*alpha*(Sqrt[r^2 + z^2] +
   Sqrt[x^2 + y^2])]*BesselJ[0, u*r]*BesselJ[0, u*x]*Cos[v*z]*
      {u, 0, Infinity}, {v, 0,Infinity},
      {r, 0, Infinity}, {x, 0, Infinity}, 
      {z, 0, 0.8},      {y, 0,  0.8}]

For different values of alpha, each time I get a value but I also get this error:

NIntegrate::eincr: The global error of the strategy GlobalAdaptive has increased more than 2000 times. The global error is expected to decrease monotonically after a number of integrand evaluations. Suspect one of the following: the working precision is insufficient for the specified precision goal; the integrand is highly oscillatory or it is not a (piecewise) smooth function; or the true value of the integral is 0. Increasing the value of the GlobalAdaptive option MaxErrorIncreases might lead to a convergent numerical integration. NIntegrate obtained 0.002014350041594919and 0.007014414732873041 for the integral and error estimates.

I would like to know if this error is affecting the value that I got, because the behavior of the results I am getting is not regular.

  • $\begingroup$ try specifying WorkingPrecision. (when you do be sure to make all the numbers in the expression exact 1.6 -> 16/10 , .8 -> 8/10 ) $\endgroup$ – george2079 Nov 28 '17 at 21:27
  • $\begingroup$ try also Method -> "AdaptiveMonteCarlo" This gives a result without any error messages at least. ( 0.01123 for alpha=1 ) $\endgroup$ – george2079 Nov 28 '17 at 21:34

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