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.