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MathGroup Archive 1995

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Help on mathieu equation needed

  • To: mathgroup at smc.vnet.net
  • Subject: [mg2141] Help on mathieu equation needed
  • From: wall at phys.chem.ethz.ch (Ernst U. Wallenborn)
  • Date: Wed, 4 Oct 1995 01:57:52 -0400
  • Organization: ETH Zuerich, Phys.Chem.Inst.

I have a 2nd order nonlinear diff. equation, which looks like

d^2w
----- + (a - 2q cos 3v) w = 0    ,(0<=v<=2 Pi)
dv^2

i.e. very similar to the mathieu equation (e.g. Abramowitz&Stegun 20.1.1)
except that cos2v is replaced by cos3v. How can i solve this in Mathematica?

I tried the usual w -> w1, w' -> w2 => 
{w1[v]' == w2[v], w2[v]' == (2q cos3v - a)w1[v]}, but DSolve and NDSolve
both complain about missing initial conditions, which is no surprise,
since the only initial condition i have is that w[2 Pi]==w[0]. So the
shooting method doesn't work.

Anybody an idea how to solve this?




---
-ernst wallenborn.

i'm not a bug.
i'm an undocumented feature.




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