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

[Tony11235]

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?

 

[Tony11235]

Nobody has any idea?

 

[neo143]

http://gershwin.ens.fr/vdaniel/Doc-Locale/Cours-Mirrored/Methodes-Maths/white/

 

[Tony11235]

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.