Finding eigenfunctions for Sturm-Liouville problems.

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Many PDE textbooks contain theoretical results regarding existence of eigenvalues and eigenfunctions for Sturm-Liouville problems but I haven't seen any that actually tell how to compute either making the theory seem not very useful. I was wondering how is can you find the eigenfunctions?

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[enter link description here][1][you can check simple worked out example of Sturm-Liouville problems in the given pdf link also find how to find eigenvalue and eigenfuction of corresponding Sturm-Liouville problems] http://www.math.iitb.ac.in/~siva/ma41707/ode7.pdf

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There is a SLEIGN$2$ (Sturm-Liouville EIGeNvalue EIGeNfunction) FORTRAN library at http://www.math.niu.edu/SL2/ . This was written by experts in the field: Paul Bailey, Norrie Everitt and Tony Zettl (with the assistance of Burt Garbow.)