Hi everybody,
I have attached an integration equation as a function of Bessel functions. The upper limit of integration is (infinite) and the lower limit is (zero). In fact, I solved it by MATLAB, but I got weird results when I just change the lower limit from zero to 0.1 or 2 and keep the upper limit as it (some value) and one more thing is that the MAXIMUM upper limit that I can reach is 10^9, beyond that amount gives me a ZERO for the whole integration!
So I think those weird results come from the existing of the variable X^5 in the denominator of the integrand and I might not use the right command of integration to integrate like this equation as a function of Bessel functions. If there is any way to represent like this integration with those Bessel terms in MATLAB, please let me know, and I will be really appreciated that help!
Thanks
Hi
you try solve it by "quadgk" command. find additional information in MATLAB Help.
Unfortunately, it does not work and shows me same weird results.
Thanks!
The expressions for phi and psi can be simplified which should help numerically. A factor that appears twice is a Wronskian defined by W(J0(x),Y0(x)) = J1(x)*Y0(x) - J0(x)*Y1(x). It so happens that such Wronskians simplify nicely to W(J0(x),Y0(x)) = 2/(pi*x). Therefore, phi = 2*Y1(x)/(pi*x) and psi = -2*J1(x)/(pi*x).
Thank you for all your replies,
I have attached the paper where the integration eq. is available in. Im looking for finding the integration of eq. 44 in the attached paper, where PHI and PSI defined in eqs. 41 & 42 respectively. The value of ( t ) in eq. 44 is any constant value as well as the values of GAMMA, K, and S in eqs 41 & 42.
I really appreciate any help to solve this integration part of eq. 44. and as I said in the question above that the maximum upper limit that I can reach is 10^9 after that No results obtained. In addition. changing the lower limit from zero to 0.1 to 3 will give me weird results!
The attached code seems to work okay as far as I can tell. I'm not seeing any strange behavior when the lower limit of 0 is increased a little bit. I can also change the upper limit to a number beyond 10^9 without trouble; however I just took the upper limit to be inf in the attached. Note that I have restricted the problem to your original integral (although simplified using the Wronskian). I also left off a factor of pi^2/4.
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