Geodesic
Finite-difference proof of the completeness of eigenfunctions of the Sturm–Liouville operator in conservative form
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 1, pp. 3-9 Cet article a éte moissonné depuis la source Math-Net.Ru

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A finite-difference method is used to prove the completeness of the eigenfunctions of the Sturm–Liouville operator in conservative form. The finite-difference schemes corresponding to the conservative Sturm–Liouville equation with various boundary conditions are shown to be self-adjoint. The accuracy and convergence of the method are analyzed, and the properties of eigenvalues and eigenvectors of the difference scheme approximating the differential equation and the boundary conditions are examined. 
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A. R. Aliev; E. Kh. Eyvazov. Finite-difference proof of the completeness of eigenfunctions of the Sturm–Liouville operator in conservative form. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 1, pp. 3-9. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_1_a0/

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