I am very late to answer my own question but I have found a solution. The practical approach to this problem was that I used a finite upper limit of integration and made use of the "trapz" function. I noticed that the exponential term was decaying very rapidly to zero and there seemed no need to integrate it to infinity. My results matched with those from the reference.
How to perform correct numerical integration of equations containing Bessel functions ?
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Torsten
2024-2-28
编辑:Torsten
2024-2-28
I suspect you want exp(-zeta^2/(4*0.0277)) instead of exp(zeta^2/(4*0.0277)) in your integrand.
And why do you add the same Bessel function two times : J0(103.562*zeta)+J0(103.562*zeta) ? This gives 2*J0(103.562*zeta) :-)
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Torsten
2024-2-28
Seems to be difficult to integrate up to Inf:
syms x
vpa(int(besselj(0,106.4202*x),x,0,Inf))
format long
fun = @(xi) besselj(0,106.4202*xi);
test = integral( fun,0,6)
testInf = integral( fun,0,Inf)
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