Help with System of nonlinear DEs

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Discussion Overview

The discussion revolves around a system of nonlinear differential equations involving current, displacement, and voltage, with a focus on finding numerical methods for solving the system. Participants explore various techniques and clarify the relationships between the variables involved.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant presents a system of nonlinear differential equations and initial conditions, seeking guidance on numerical techniques for solving them.
  • Another participant questions the independence of the variables i and x.
  • A participant confirms that i, x, and v are independent functions of time and suggests using numerical methods, specifically mentioning the Runge-Kutta method.
  • There is a proposal to solve for i given x as a second-order differential equation in v, emphasizing the use of numerical methods.
  • A later reply expresses a preference for a second-order Runge-Kutta method due to the need for fast results with moderate accuracy.

Areas of Agreement / Disagreement

Participants generally agree on the independence of the variables and the necessity of numerical methods, but there is no consensus on the specific method to be used, with differing opinions on the appropriateness of Runge-Kutta.

Contextual Notes

The discussion does not resolve the implementation details of the proposed numerical methods or the specific challenges posed by the meshed equations.

Jay Carp
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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:
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Are i and x independent ?
 
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?
 
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.
 
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
 

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