Solving non-linear equations simultaneously with DE's using Euler integration

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Discussion Overview

The discussion revolves around the challenge of solving a set of 15 non-linear equations simultaneously with ordinary differential equations (ODEs) using Euler's method, specifically avoiding the use of MATLAB's ode45 function. The context includes both theoretical and practical considerations related to dynamic systems and numerical integration methods.

Discussion Character

  • Technical explanation
  • Homework-related
  • Debate/contested

Main Points Raised

  • One participant seeks guidance on combining non-linear equations with ODEs using Euler's method, expressing a need for a solution to a dynamic process.
  • Another participant questions the necessity of using Euler's method, suggesting that the inquiry might relate to real-time applications or speed requirements.
  • A participant mentions their previous experience with the assignment and notes that their professor indicated that ode45 would not work, without providing a reason.
  • There is a suggestion that Euler's method may not be the best choice, with a participant expressing surprise if it was recommended by the professor.
  • Concerns are raised about the potential inefficiency of ode45 if it requires very small step sizes to meet error tolerances, and the accuracy of solutions obtained through Euler's method is questioned.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of Euler's method versus ode45, with some questioning the reliability of Euler's method for achieving accurate results. The discussion remains unresolved regarding the best approach to take.

Contextual Notes

There are indications of uncertainty regarding the stiffness of the equations involved and the implications this may have for the choice of numerical methods. The limitations of Euler's method in terms of accuracy and efficiency are also noted but not fully explored.

Jigby
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I have 15 equations with 15 unknowns describing a dynamic process. I would like to know how I can conbine solving non-linear equations together with ordinary differential equations (1st and 2nd order) simultaneously, without using ode45, but Euler's method.
 
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Jigby said:
I have 15 equations with 15 unknowns describing a dynamic process. I would like to know how I can conbine solving non-linear equations together with ordinary differential equations (1st and 2nd order) simultaneously, without using ode45, but Euler's method.

Why would you want to do that? Are you doing a real time application or something or a homework question. Do you require very fast integration? Anyway, you can always write your own function. Euler's method is pretty basic.
 
Thanks John, I will try that!
My program is based the dynamic response of a system in the time domain. It was for an assignment last year, but I never quite got it to work so I thought I would try again. My prof told us ODE 45 would not work, he didn't say why though.
 
Jigby said:
Thanks John, I will try that!
My program is based the dynamic response of a system in the time domain. It was for an assignment last year, but I never quite got it to work so I thought I would try again. My prof told us ODE 45 would not work, he didn't say why though.

Did he say the Euler's method would work? If so I'm surprised. You know that you can give ODE45 a set of points to calculate the state values at.
 
John Creighto said:
Did he say the Euler's method would work? If so I'm surprised. You know that you can give ODE45 a set of points to calculate the state values at.

i agree with John,and whether you eqtion a stiff one?
 
Yeah, MATLAB has some stiff solvers as well. One thing that could happen with ODE45 is it could take too long to integrate if it ends up needing to take too small a step size to get the required error tolerance. One way to get around this is to decrease the error tolerances in ODE45. Euler's method may get you a solution but I don't know how you can be sure it is sufficiently accurate.
 

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