How to Solve Sturm-Liouville Problems to Find Eigen Value and Eigenfunction?

  • Context: Graduate 
  • Thread starter Thread starter HansLee
  • Start date Start date
Click For Summary
SUMMARY

The discussion focuses on solving Sturm-Liouville problems to determine eigenvalues and eigenfunctions, specifically the equation x²y'' + 2xy' + λy = 0 with boundary conditions y(0) = 0 and y(e²) = 0. A participant initially struggled with the problem but successfully found the solution after reconsidering the trial function y = xⁿ. This highlights the importance of revisiting assumptions and calculations in mathematical problem-solving.

PREREQUISITES
  • Understanding of Sturm-Liouville theory
  • Familiarity with differential equations
  • Knowledge of boundary value problems
  • Experience with trial functions in eigenvalue problems
NEXT STEPS
  • Study Sturm-Liouville theory in detail
  • Explore methods for solving boundary value problems
  • Learn about different trial functions for eigenvalue problems
  • Investigate numerical methods for approximating eigenvalues and eigenfunctions
USEFUL FOR

Mathematicians, physics students, and engineers dealing with differential equations and eigenvalue problems will benefit from this discussion.

HansLee
Messages
4
Reaction score
0
I have a problem about Sturm-Liouville, and i can't solve it, maybe someone can help me

x2 y''+ 2xy'+ λy=0

and y(0)=0, y(e2)=0

What is the eigen value and eigenfunction of the equation?
 
Physics news on Phys.org
Has one tried y=xn?
 
Ooo thanks, actually I have tried y=xn before, but there's a miscalculate. But when I see ur suggestion, I tried once again and got the answer. Thanks
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 45 ·
2
Replies
45
Views
9K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 13 ·
Replies
13
Views
4K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
11
Views
5K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K