Timeline for How to solve this integral equation using Mathematica?
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| S Apr 17, 2020 at 13:26 | history | bounty ended | CommunityBot | ||
| S Apr 17, 2020 at 13:26 | history | notice removed | user35588 | ||
| Apr 14, 2020 at 20:29 | answer | added | Steffen Jaeschke | timeline score: 0 | |
| Apr 14, 2020 at 14:28 | answer | added | Alex Trounev | timeline score: 5 | |
| Apr 12, 2020 at 13:55 | comment | added | Alex Trounev |
@BruceLee There is no problem to make a code for numerical solution of the Case 1. But for the Case 2 we need some regularization since with Mathematica we can handle only Cauchy type "PrincipalValue" (as in a Case 1).
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| Apr 11, 2020 at 6:17 | comment | added | xzczd♦ | As mentioned above, this is the first term of a Fourier sine series expansion: $\rho(\beta)=c_1 \sin(\beta/2 +\pi/2)+c_2 \sin(2(\beta/2+\pi/2))+…$ | |
| Apr 11, 2020 at 6:02 | comment | added | user35588 |
@xzczd Why this particular integral? It just shows that Sin[b/2 + Pi/2] isn't the solution, right? I would suggest to cross check any method with Case 1, it might be helpful. I don't think that the question itself is wrong.
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| Apr 11, 2020 at 3:08 | comment | added | xzczd♦ |
I suspect the question itself is wrong. Assuming $\rho(\beta)$ can be expanded as Fourier sine series on $[-\alpha_c, \alpha_c]$, take $\alpha=\pi/2$, $\alpha_c=\pi$, and compute the first term of the series expansion, Integrate and NIntegrate both complain the integral doesn't converge: Integrate[(Cot[(Pi/2 - b)/2] Sin[b/2 + Pi/2])/Sin[(Pi/2 - b)/2], {b, -Pi, Pi}, PrincipalValue -> True], NIntegrate[(Cot[(Pi/2 - b)/2] Sin[b/2 + Pi/2])/Sin[(Pi/2 - b)/2], {b, -Pi, Pi/2, Pi}, Method -> PrincipalValue].
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| Apr 10, 2020 at 20:53 | history | edited | user35588 | CC BY-SA 4.0 |
changed a minus sign
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| Apr 10, 2020 at 19:28 | comment | added | user35588 | @xzczd Fine with either, however in both cases I would like to see a plot of the $\rho(\beta)$ with $\beta$ for some values of $\lambda$. | |
| Apr 10, 2020 at 4:53 | comment | added | xzczd♦ | "I am fine with either an exact answer or an approximate one." By "approximate one" do you mean a symbolic solution like series solution, or numeric solution? | |
| Apr 10, 2020 at 3:00 | history | tweeted | twitter.com/StackMma/status/1248445686829514754 | ||
| S Apr 10, 2020 at 0:53 | history | bounty started | CommunityBot | ||
| S Apr 10, 2020 at 0:53 | history | notice added | user35588 | Draw attention | |
| Apr 8, 2020 at 0:19 | history | asked | user35588 | CC BY-SA 4.0 |