NIntegrate and double integral -- very slow

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• Subject: [mg132436] NIntegrate and double integral -- very slow
• From: bluesaturn <bluesaturn.at.kellnerweg.de at gmail.com>
• Date: Sat, 15 Mar 2014 03:46:25 -0400 (EDT)
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```Dear all
I am trying to model something. This involves oscillating function
(BesselJ0, BesselJ1) over that I have to integrate. An example is shown
below.
Mathematica is not able to manage to calculate the last three lines, not
even overnight (12-14h). I don't think there is a simple analytical
solution that is why I tried the numerical approach.
How can I speed up the calculations, please?  For example the line with
the Table-Command. Ideally I would like to have more than just 26 points.

Kind regards
B.

%%%%%%%%%%%%%%%%%%%%%%% Example code

formfactorrodx[q_, alpha_] :=
lengthcylinder*Sinc[q*alpha*lengthcylinder/2]*rhoRodcontrast*2*Pi*
acylinder*BesselJ[1, q*acylinder*Sqrt[1 - alpha^2]]/(q*Sqrt[1 - alpha^2])

nx[rcx_] := ((2*Abs[beta])/(kappanormal*rcx*Cos[beta*Log[rcx/RM]]))^2*
nR0;

formfactorcounterionx[q_, alpha_, rcx_] :=
lengthcylinder*Sinc[q*alpha*lengthcylinder/2]*rhoPBsolvent*nx[rcx]*
BesselJ[0, q*rcx*Sqrt[1 â?? alpha^2]]*2*Pi*rcx;

intensityRodCounterions[q_?NumericQ] :=
NIntegrate[
2*fp*formfactorcounterionx[q, alpha, rcx]*
formfactorrodx[q, alpha], {rcx, acylinder, router}, {alpha, 0,
1 - chiint}, Method -> {"MonteCarlo", "MaxPoints" -> 10^10}];

Table[intensityRodCounterions[1*10^(-1)*10^(9)*i], {i, 26}]

ListLinePlot[
Table[intensityRodCounterions[q], {q, 1*^-1*1*^9, 2.6*1*^9, 26}]]

LogLogPlot[intensityRodCounterions[q], {q, 1*^-1*1*^9, 2.6*1*^9}]

```

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