MathieuCharacteristicA strange behaviour
- To: mathgroup at smc.vnet.net
- Subject: [mg115087] MathieuCharacteristicA strange behaviour
- From: "Jose M. Castelo" <jocasa at alumni.uv.es>
- Date: Thu, 30 Dec 2010 06:29:03 -0500 (EST)
Hi!
I'm working with the Mathematica function 'MathieuCharacteristicA[r,q]'
which gives the characteristic value for even Mathieu functions with
characteristic exponent r and parameter q.
After testing with various commands which deal with computation
precision I have been unable to obtain a good behaviour of the function
for some values of q and some ranges of r. You can see that the function
does strange things by ploting it against r:
Plot[MathieuCharacteristicA[r, 100], {r, 10, 17}]
Plot[MathieuCharacteristicA[r, 8652.34], {r, 140, 150}]
The curve jumps abruptly where it should be smooth. I don't mean the
zones where the function is staircase like, I know that is the right
shape it should have. The same happens with 'MathieuCharacteristicB[r,q]'.
Perhaps I am missing some precision detail in the plot, or in the
selfsame function, though I have tried to solve it unsuccessfully by
using precision related commands. Perhaps it is a bug.
Could you tell me if you get the same results? Maybe you can throw some
light on how to get it work correctly, as the very same
'MathieuC[a,q,z]' and 'MathieuS[a,q,z]' functions depend on the
characteristic value 'a' directly, not on the characteristic exponent
'r' as I think should be better. In that way they inherit the error of
the characteristic value computation.
If this is not the right place to post a message about Mathematica bugs,
please let me know where to post it.
Thanks a lot,
Jose