Convergance and Laplace transforms

Click For Summary
SUMMARY

The discussion centers on the applicability of the final value theorem in determining the convergence or divergence of specific differential equations. The user questions whether this theorem yields results consistent with identifying positive or negative real roots. Despite personal experimentation, the user finds their results inconclusive and expresses difficulty in locating relevant literature on the topic, particularly due to the commonality of the terms involved.

PREREQUISITES
  • Understanding of the final value theorem in control theory
  • Familiarity with ordinary differential equations (ODEs)
  • Knowledge of convergence and divergence criteria for differential equations
  • Basic grasp of Laplace transforms and their applications
NEXT STEPS
  • Research the final value theorem in the context of control systems
  • Study convergence criteria for ordinary differential equations
  • Explore the relationship between Laplace transforms and differential equation solutions
  • Investigate literature on advanced techniques for solving ODEs
USEFUL FOR

Students and professionals in mathematics, engineering, and physics who are dealing with ordinary differential equations and seeking to understand convergence behavior through the final value theorem and Laplace transforms.

heatgrad
Messages
2
Reaction score
0
Hi,
Is the final value theorem an appropriate way to deduce if a specific differential equations converges or diverges?
 
Physics news on Phys.org
What I guess I mean is, does it offer the predict the same results as finding positive or negative real roots?

I've tried it out for myself a few times and my own results are...inconclusive. But I'm kind of getting back into this method of dealing with ODEs after letting it lie for over a year. And finding literature about it largely proves unfruitful, especially because describing the information I want includes very common terms or too many terms, causing a tidal wave of unwanted results.
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 8 ·
Replies
8
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K