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MathGroup Archive 2008

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Mathematica and Mathieu DEQ Results?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg91134] Mathematica and Mathieu DEQ Results?
  • From: amzoti <amzoti at gmail.com>
  • Date: Thu, 7 Aug 2008 04:39:05 -0400 (EDT)

Hi All,

1. I am using Mathematica, to solve the following DEQ:
DSolve[x''[t] + (4[Pi]^2 - 2((-Pi^2/5) Cos[2 (Pi t)/100])))x[t] == 0,
x[t], t] (1)

 This results in a solution of even and odd Mathieu functions as
follows:

 x[t] = C[1] MathieuC[40000, -2000, Pi*t/100] + C[2] MathieuS[40000,
 -2000, Pi*t/100]

 2. However, according to <http://mathworld.wolfram.com/
MathieuDifferentialEquation.html,
 the result is:

 x[t] = C[1] MathieuC[4 Pi ^2, -Pi^2/5, Pi*t/100] + C[2] MathieuS[4 Pi
 ^2, -Pi^2/5, Pi*t/100] (2)

 a. I am confused why I am getting these totally different results.

 b. The paper I am reading <epsppd.epfl.ch/Roma/pdf/P2_091.pdf shows
 three different plots that match with (2) - where I am able to
 duplicate the results/plots of the paper exactly using this method.

 Can someone out there shed light on why this is the case?

 Why can't Mathematica get the same result (or is it that the DEQ does
not have a unique solution based on some properties of Mathieu
functions)?

 Any insights are appreciated!

 ~A


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