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DSolve bug for complicated forcing functions in a 2nd order ODE

  • To: mathgroup at
  • Subject: [mg122394] DSolve bug for complicated forcing functions in a 2nd order ODE
  • From: Dan Dubin <ddubin at>
  • Date: Thu, 27 Oct 2011 06:31:28 -0400 (EDT)
  • Delivered-to:

Folks -- reporting a bug in DSolve, I think. The following Module solves 
a 2nd order differential equation with periodic forcing, written as a 
Fourier series. The number of Fourier coefficients kept  in the series 
is M. For M less than or equal to 40, the solution is correct, but for M 
greater than 40 it starts to go wrong. Try M=41, for instance.  The 
resulting solution no longer satisfies the ODE. Any ideas what is 
happening here? 

PS[M_] := Module[{},
  T = 1/2;
  =CF=89[n_] = 2 Pi n/T;
  f[n_] = 1/T Integrate[1 Exp[I =CF=89[n] t], {t, 0, 1/4}];
  f[0] = Limit[f[n], n -> 0];
  fapprox[t_] = Sum[f[n] Exp[-I =CF=89[n] t], {n, -M, M}];
  s = DSolve[{x''[t] + 16 =CF=80^2 x[t] == fapprox[t], x[0] == 0, x'[0] == 0},
    x[t], t];
  xs[t_] = x[t] /. s[[1]];
  xs''[t] + 16 Pi^2 xs[t] - fapprox[t] // Simplify]

Prof. Dan Dubin
Dept of Physics, UCSD La Jolla CA 92093-0319
858-534-4174 fax: 858-534-0173
ddubin at

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