Author 
Comment/Response 
FRanc Solina Gilbert

10/05/05 4:48pm
Hi yehuda :),
Thanks for the advices :). I start understanding Mathematica. I have found a posible solution to my problem. Since g[t] is my system's input (vibration initiator) and I replace g[t] by an Mathematica interpolated polynomial of the kind
\!\(HSE[a_?NumberQ, b_?NumberQ, c_?NumberQ, d_?NumberQ] := Block[{sol,
f}, sol = \(NDSolve[{\((a + b\ Abs[f[t]] + c\
f[t]\^2 + d\ Abs[f[t]\^3])\)\ f[
t] + c\ \(f'\)[
t] == \(0.2200821389305352`\) +
2.6933892154486747`\ t  2.898740511629984`\ t\^2 +
1.4915822724657741`\ t\^3\ , f[0] == 0}, f, {t,
0, 500}, Method > "\<Automatic\>"]\)[\([1]\)];
Plus @@ Apply[\((f[#1]  #2)\)^2 &, data, {
1}] /. sol]; NMinimize[HSE[A, B, C, D], {A, B, C, D}, \
Method > "\<NelderMead\>"]\)
then I get after some error massages a solution to my problem. Mathematica does a least square fit of the parameters (a,b,c,d). Now, lets come to the error massages:
NDSolve::ndcf. Repeated convergence test failure at t == 123.06374629313223; unable to continue.
NDSolve::ndsz: At t == 18.585850047911073`, step size is effectively zero; singularity or stiff system suspected
I assume that the singularity in my system result from a polynomial attempt. Because, when I replace the right side of the equation with, a periodic attempt of the kind Sin[t]+(Sin[t])^2, then Mathematica finds automatically a least square fit to my problem. Now the system is not singular anymore. Normally Mathematica tries a polynomial interpolation. I would like to use a Fourier interpolation. I concentrate myself at the moment to periodic input signals. So a Fourier analysis is something to thing about. Is there a possibility to do that with the aim to get a peridical interpolation function for g[t]?
Regards, Franc
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