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Goofy
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Numerical integration Nintegrate bessel functions Getting error NIntegrate::eincr; how should I deal with it?

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]*
   Cos[y*v]*(Cos[Pi*z/1.6]*Cos[Pi*y/1.6])^2, 
      {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 0.002014350041594919 and 0.007014414732873041 for the integral and error estimates.

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 0.002014350041594919 and 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 data thatresults I gotam getting is not regular.

Thank you for your help

Numerical integration Nintegrate bessel functions

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]*
   Cos[y*v]*(Cos[Pi*z/1.6]*Cos[Pi*y/1.6])^2, 
      {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 0.002014350041594919 and 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 data that I got is not regular.

Thank you for your help

Getting error NIntegrate::eincr; how should I deal with it?

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]*
   Cos[y*v]*(Cos[Pi*z/1.6]*Cos[Pi*y/1.6])^2, 
      {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 0.002014350041594919 and 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.

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george2079
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I am trying to solve an integral using NintegrateNIntegrate:

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]*
   Cos[y*v]*(Cos[Pi*z/1.6]*Cos[Pi*y/1.6])^2, 
      {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 0.002014350041594919 and 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 data that I got is not regular.

Thank you for your help

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]*  Cos[y*v]*(Cos[Pi*z/1.6]*Cos[Pi*y/1.6])^2, {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 0.002014350041594919 and 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 data that I got is not regular.

Thank you for your help

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]*
   Cos[y*v]*(Cos[Pi*z/1.6]*Cos[Pi*y/1.6])^2, 
      {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 0.002014350041594919 and 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 data that I got is not regular.

Thank you for your help

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