Geodesic
On the Computation of Eigenfunctions and Eigenvalues in the Sturm--Liouville Problem
Matematičeskie zametki, Tome 97 (2015) no. 4, pp. 604-608

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We present the variational method for finding the eigenfunctions and eigenvalues in the Sturm–Liouville problem with Dirichlet boundary conditions; the method is based on the proposed functional. As a test example, we consider the potential $\cos(4x)$. Also computations for two functions $\sin((x-\pi)^2/\pi)$ and a high nonisosceles triangle are given.
Keywords: variational method, functional, eigenfunction, eigenvalue, Dirichlet boundary condition, the function $\sin((x-\pi)^2/\pi)$, the function $\cos(4x)$, nonisosceles triangle, random search method, Wolfram Research, “Nminimize” procedure, algorithm.
Mots-clés : Sturm–Liouville problem 
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     author = {M. M. Khapaev and T. M. Khapaeva},
     title = {On the {Computation} of {Eigenfunctions} and {Eigenvalues} in the {Sturm--Liouville} {Problem}},
     journal = {Matemati\v{c}eskie zametki},
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M. M. Khapaev; T. M. Khapaeva. On the Computation of Eigenfunctions and Eigenvalues in the Sturm--Liouville Problem. Matematičeskie zametki, Tome 97 (2015) no. 4, pp. 604-608. http://geodesic.mathdoc.fr/item/MZM_2015_97_4_a9/