A system of two second order differential equations

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Discussion Overview

The discussion revolves around methods for solving a system of two coupled second order differential equations. Participants explore the requirements for solving these equations by hand and the implications for coding solutions without using built-in functions from software like MATLAB. The initial conditions involve zero displacement and velocity, with acceleration dependent on pressure as a function of time.

Discussion Character

  • Exploratory, Technical explanation, Homework-related, Mathematical reasoning

Main Points Raised

  • One participant inquires about the best method to solve coupled second order differential equations by hand and through custom coding.
  • Another participant asks for clarification on whether the equations are ordinary, linear, and homogeneous.
  • A different participant suggests that if it is a computational project, a simple Euler integration method could be used after converting the equations into first order form, recommending a comparison with results from a Runge-Kutta 4 (RK4) method.
  • A later reply indicates that the participant successfully converted the equations into four first order equations and found that it worked well.

Areas of Agreement / Disagreement

The discussion does not present a consensus on the best method to solve the equations, as participants are exploring different approaches and clarifications. Multiple views on the computational methods remain, and the discussion is still open-ended.

Contextual Notes

There are limitations regarding the specifics of the differential equations, such as their classification (ordinary, linear, homogeneous) and the initial conditions related to pressure dependence, which are not fully resolved.

Who May Find This Useful

Individuals interested in solving coupled differential equations, particularly in a computational context, as well as those looking for coding strategies for numerical integration methods.

jeffro06
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I was wondering what the best method is to solve two second order differential equations that are coupled. I need to solve it by hand and write my own code so I cannot use built in functions in matlab, etc. At time (0), displacement and velocity are 0 with an initial acceleration which is dependent on pressure as a function of time.
 
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Perhaps a little more detail would be helpful. Are these ordinary DEs? Linear? Homogeneous?
 
...and...

Is it a computational project?

What language do you use?

fwiw, if it is, just write a simple Euler integration code (after putting the equations into first order form), see if it works and then compare with results from an RK4 code...
 
I didn't know that I could put them into 4 first order equations, but I did it and it worked fine. Thank you.
 

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