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

• To: mathgroup at smc.vnet.net
• Subject: [mg122394] DSolve bug for complicated forcing functions in a 2nd order ODE
• From: Dan Dubin <ddubin at ucsd.edu>
• Date: Thu, 27 Oct 2011 06:31:28 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```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 = 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, x' == 0},
x[t], t];
xs[t_] = x[t] /. s[];
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 ucsd.edu

```

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