Find the Principal Eigenvalue of Sturm-Liouville Problem with Rayleigh Quotient

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Homework Help Overview

The discussion revolves around finding the principal eigenvalue of a Sturm-Liouville problem using the Rayleigh quotient. The specific differential equation presented is u'' + (λ - x²)u = 0, with boundary conditions u(0) = 0 and u'(1) = 0.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply the Rayleigh quotient method but expresses uncertainty after stating the integration by parts step. Other participants inquire about directions and express a lack of responses.

Discussion Status

The discussion appears to be in an early stage, with the original poster seeking assistance and clarification on the method. There are indications of attempts to engage others, but no substantial guidance or consensus has emerged yet.

Contextual Notes

Participants note the need for further clarification on the steps involved in applying the Rayleigh quotient, as well as the boundary conditions that may influence the approach.

Tony11235
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Use the Rayleight quotient to find a good approximation for the principal eigenvalue of the Sturm-Liouville problem.
u'' + (\lambda - x^2)u = 0
0 < x < 0
u(0) = u'(1) = 0
Any help?
 
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Nobody has any idea?
 
http://gershwin.ens.fr/vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/
 
Last edited by a moderator:
neo143 said:
http://gershwin.ens.fr/vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/

Directions?


Back to the problem, I know that you multiply both sides by u, integrate by parts, and then solve for lambda, after that I'm stuck.
 
Last edited by a moderator:

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