Author Topic: 4.2 Example 4(periodic)  (Read 136 times)

Tianyi Zhang

  • Jr. Member
  • **
  • Posts: 9
  • Karma: 0
    • View Profile
4.2 Example 4(periodic)
« on: November 02, 2016, 02:10:55 PM »
$$X^{''} + \lambda X = 0$$
with condition  $$X(0) = X(l), X^{'}(0) = X^{'}(l)$$
how to get the answer $$\lambda_{2n-1} = \lambda_{2n} = (\frac{n\pi}{2l})^{2}$$ and the corresponding eigenfunctions?

Victor Ivrii

  • Administrator
  • Elder Member
  • *****
  • Posts: 1332
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
Re: 4.2 Example 4(periodic)
« Reply #1 on: November 02, 2016, 04:58:40 PM »
We did it on lectures: you need to solve constant coefficients ODE and find when and how many non-trivial solutions it has satisfying boundary conditions

http://www.math.toronto.edu/courses/apm346h1/20169/PDE-textbook/Chapter4/S4.2.html#example-4.2.2

Anyone wants to post details here?

PS. It should be $=(\frac{2\pi n }{l})^2$. I will fix misprint tonight.
« Last Edit: November 02, 2016, 05:32:58 PM by Victor Ivrii »