Help with System of nonlinear DEs

In summary, the conversation is about solving a system of nonlinear differential equations involving displacement (x), time (t), current (i), capacitance (C), and voltage (v). The initial conditions are also given. The question is whether or not Euler's method can be used and what numerical technique is needed. It is suggested to use Runge Kutta, specifically a second order method for faster results. One person also mentions that the variables i, x, and v are all independent functions of t.
  • #1
Jay Carp
3
0
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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  • #2
Are i and x independent ?
 
  • #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?
 
  • #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.
 
  • #5
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
 

1. What is a system of nonlinear differential equations?

A system of nonlinear differential equations is a set of equations that describe the relationships between multiple variables and their rates of change. Nonlinear means that the equations do not follow a simple linear pattern, and may involve exponents, logarithms, or other nonlinear functions.

2. How do you solve a system of nonlinear differential equations?

The process of solving a system of nonlinear differential equations involves finding a set of values for the variables that satisfy all of the equations. This can be done using analytical or numerical methods, such as substitution, elimination, or using software programs like MATLAB or Mathematica.

3. What are some real-world applications of systems of nonlinear differential equations?

Systems of nonlinear differential equations are commonly used in fields such as physics, engineering, and economics to model complex systems that involve multiple variables and their rates of change. Some examples of real-world applications include population growth, chemical reactions, and electrical circuits.

4. What are some challenges of working with systems of nonlinear differential equations?

One of the main challenges of working with systems of nonlinear differential equations is that they often do not have a simple analytical solution, making it necessary to use numerical methods. Additionally, these systems can be highly sensitive to initial conditions and small changes in the equations can lead to drastically different outcomes.

5. What are some strategies for solving systems of nonlinear differential equations?

There are several strategies that can be used to solve systems of nonlinear differential equations. These include linearization, where the system is approximated by a set of linear equations, or using techniques such as separation of variables or Laplace transforms. Choosing an appropriate method depends on the specific equations and the desired level of accuracy.

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