Help with System of nonlinear DEs

[Jay Carp]

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!

 

[Eynstone]

Are i and x independent ?

 

[Jay Carp]

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?

 

[Eynstone]

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.

 

[Jay Carp]

Eynstone:

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.

J