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I'm trying to plot a Fourier transform of solution of differential equation. I have tried with:

Plot[Evaluate@
  Abs[FourierTransform[
    Re@Evaluate[
      p[t] /. NDSolve[{p'[s] == 1 + (-1.3 + I*10 + p[s])*p[s], 
         p[0] == 0}, p, {s, 0, 10}, MaxSteps -> 100000]], 
    t, \[Omega]]], {\[Omega], 0, 100}, PlotRange -> All]

without success.

What am I doing wrong?

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  • 1
    $\begingroup$ The "?" button in the edit box gives tips on formatting, such as how to format code. $\endgroup$
    – Michael E2
    Feb 28, 2013 at 13:21
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    $\begingroup$ Why not use Fourier? ff = p[t] /. NDSolve[{p'[s] == 1 + (-1.3 + I*10 + p[s])*p[s], p[0] == 0}, p, {s, 0, 10}, MaxSteps -> 100000][[1]] and Table[ff, {t, 0, 10, 10/256}] // Fourier // Abs // Rest // Flatten // ListLogPlot[#, PlotRange -> All] & $\endgroup$
    – chris
    Feb 28, 2013 at 13:34

1 Answer 1

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You can solve the equation analytically :

sol[s_] = DSolve[{p'[s] == 1 + (-13/10 + I*10 + p[s])*p[s], p[0] == 0}, p[s], {s}][[1, 1, 2]]
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    $\begingroup$ But an analytical Fourier transform for the function seems to be still impossible? $\endgroup$
    – xzczd
    Feb 28, 2013 at 13:57
  • 2
    $\begingroup$ I think so; also notice the function flattens to a constant for large argument. $\endgroup$ Feb 28, 2013 at 14:02
  • 1
    $\begingroup$ Oh, that's interesting! $\endgroup$
    – xzczd
    Feb 28, 2013 at 14:17

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