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comment Numerical inverse Laplace-Hankel transform
Thanks for clarification, now it's clearer. BTW, what's your Mathematica version? I just tested in v9.0.1 and v10.4.1 (Wolfram Cloud), Mathematica is able to correctly find the closed form of Hankel transform of all 3 residues: i.stack.imgur.com/24U1a.png
Apr
29
comment Numerical inverse Laplace-Hankel transform
Oh, finally here comes an answer! (I had almost accepted the reality that my 500 reputation would go with wind...) Then, sorry for my weak basis of complex analysis, but can you elaborate a little on the "The Bromwich contour then can be distorted to yield a solution consisting of the three Residues plus integrals of the discontinuities along the four branch cuts" part?
Apr
27
comment Solving equations but cannot define argument
Works fine here: i.stack.imgur.com/fA9np.png I guess you forgot to Clear some of the variables?
Apr
27
comment Solving equations but cannot define argument
What's the definition of H?
Apr
27
comment Multiply integrand with -1, and the precision changes?
@Xavier OK, done.
Apr
27
comment Numerical inverse Laplace-Hankel transform
@Lukas Thanks for the comment, but sadly "SymbolicProcessing" -> 0 seems not to help here... for this integral the only 2 available methods seem to be "ExtrapolatingOscillatory" and "LevinRule". "SymbolicProcessing" isn't an option for "LevinRule", and doesn't improve the speed of "ExtrapolatingOscillatory", what's more, because of a bug mentioned here, one will be unable to adjust the MaxRecursion option if Method -> {"ExtrapolatingOscillatory", "SymbolicProcessing" -> 0} is used.
Apr
26
comment KernelObject appears dead problem
You still got an answer after these warning? In my case MMA didn't return an answer for several days so I finally quit the kernel.
Apr
26
comment KernelObject appears dead problem
I used to observe this warning when doing some... heavy parallel computing with v8.0.4, not sure about the exact reason also.
Apr
25
comment Multiply integrand with -1, and the precision changes?
@Xavier Interesting. Using the code in the update of this answer, I found that in this case NIntegrate internally switches to "LevinRule", and the output is indeed the same as that with option , Method -> "LevinRule". How about giving an answer?
Apr
23
comment Multiply integrand with -1, and the precision changes?
@J.M. I also tried manually implement "ExtrapolatingOscillatory", and the problem doesn't show up in my (much slower) implementation: zero[i_] := Piecewise[{{BesselJZero[0, i], i > 0}}];separatepmhankel[p_?NumericQ, sign : 1 | -1, i_?NumericQ, prec_] := NIntegrate[sign ξ BesselJ[0, ξ] f[p, ξ], {ξ, zero@i, zero[i + 1]}, WorkingPrecision -> prec, MaxRecursion -> 40]; manualpmhankel[p_, sign_: 1, prec_: 16] := NSum[separatepmhankel[p, sign, i, prec], {i, 0, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> prec]; manualpmhankel[32, #, 32]&/@{1,-1} // AbsoluteTiming
Apr
23
comment Multiply integrand with -1, and the precision changes?
@Searke Thanks for the response. (1) With "SymbolicProcessing->0" the problem remains: pmhankelTest[p_, sign_: 1, prec_: 16] := NIntegrate[sign ξ BesselJ[0, ξ] f[p, ξ], {ξ, 0, ∞}, WorkingPrecision -> prec, Method -> {"ExtrapolatingOscillatory", "SymbolicProcessing" -> 0}];pmhankelTest[32, #, 32] & /@ {-1, 1} (2) I tried IntegrationMonitor mentioned in this answer, the {"Boundaries", "Dimension", "Error", "GetRule", "Integrand"} etc. seems to be all the same, and the only difference between "Integral" is the sign.
Apr
16
comment Compute inverse Laplace transform with Integrate
Though not a complete answer, thanks for your effort :)
Apr
15
comment Why can't I change the value of MaxRecursion in NIntegrate when integrating BesselJ?
@ShutaoTANG Mainly because I'm still in v9 and want to make the post self-contained so not that willing to use LetL etc. in this sample. You can have a look at this post: mathematica.stackexchange.com/a/54874/1871
Apr
14
comment Why can't I change the value of MaxRecursion in NIntegrate when integrating BesselJ?
@J.M. I did hesitate for a while but finally decided to post this answer. Anyway this integral contains BesselJ and if you tried something like uztran[specialp, WorkingPrecision -> 64, MinRecursion -> 20, MaxRecursion -> 40] you'll see the same warning as that mentioned in the question.
Apr
14
comment Export a plot to Excel
Possible duplicate of Plot, extract data to a file
Apr
14
comment Why does ContourPlot refuse to draw all 4 quadrants whenever fractional powers are in the implicit function?
Possible duplicate of Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)
Apr
14
comment Integrate boundaries defined as equations
As mentioned by @Dr.belisarius , what's incorrect here is the original text. (Or at least it has followed a very uncommon rule for the order of integration variables.) Anyway, Abs[r12 - r13], r12 + r13 can only be bounds of r23.
Apr
14
comment triple NIntegrate fails
I think kB represents Boltzmann constant? If so, why it's 0.001872041?
Apr
14
comment NIntegrate crashes without error message when using high precision integrand with non-zero tailing digits
Works fine in v9.0.1. Have you reported this to WRI?
Apr
11
comment Possible Bug in LinearSolveFunction with Sparse Vectors
Also reproduces in v8.0.4 and v9.0.1, win10 64bit.