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Highly nonlinear ODE

  1. Dec 4, 2015 #1
    I have an equation of motion given by
    $$f(z(t),t) = \frac{d^2z}{dt^2} + A\frac{dz}{dt} + B $$
    where
    $$f(z(t),t) = [(\frac{C}{z^2+C^2})^2-(\frac{D}{z^2+D^2})^4]^2(1+cos(wt))$$
    and ##A,B,C,D,## and ##w## are constants

    Is it possible to solve this for ##z(t)##? I have been solving it numerically using Matlab's ODE solver but as this model is used to fit a set of experimental data (constants ##A## and ##B## are varied until a reasonably small error is achieved between this and the experimental data) it would greatly reduce computational time if a solution or even a close approximation can be found.

    I know from numerically solving ##z(t)## that it is periodic so there must be a Fourier series that can be used to find a solution. I have basic knowledge of Fourier analysis and since ##f## is a function of ##z## and ##t##, and ##z## is dependent on ##t##, I'm unsure how to do this. If someone could point me in the right direction it would be much appreciated.
     
  2. jcsd
  3. Dec 9, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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