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Help with System of nonlinear DEs

  1. Jul 9, 2010 #1
    Hello everybody. I have a quick question. I have the following system of nonlinear differential equations:

    (di/dt)(x)+(x^2 - dx/dt)(i)+ v(t) =0 _ _ _1

    dv/dt = i/C _ _ _2

    I know my Initial Conditions: i(0) = 0, di(0)/dt = 0, x(0) = L, dx(0)/dt = 0, v(0)=V

    PS- x is displacement, t is time, i is current, C is capacitance, v is cap voltage.

    Does anyone have any clues whatsoever on how to solve this? Can I use Euler's method somehow? What kind of numerical technique do I need??

    I would greatly appreciate somebody's help! Thanks all!
    Last edited: Jul 9, 2010
  2. jcsd
  3. Jul 12, 2010 #2
    Are i and x independent ?
  4. Jul 12, 2010 #3
    Yes, i and x are, and so is v. They are all functions of t...
    I was told to use Runge Kutta by a friend, but am still not sure how to implement it for meshed equations like this. Anyone have any hints?
  5. Jul 13, 2010 #4
    If x & i are independent, we can solve for i for a given x ( as a differential equation of second order in v). The best way would be to use numerical methods.
  6. Jul 13, 2010 #5

    Thanks for the pointers! What numerical method would you use? I was going to use just a second order Runge-Kutta, since I need fast results with not too much accuracy.

    Once again, thanks bud.

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