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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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/

[1] L. D. Akulenko, S. V. Nesterov, “Effektivnyi metod issledovaniya kolebanii suschestvenno neodnorodnykh raspredelennykh sistem”, Prikl. matem. mekh., 61:3 (1997), 466–478 | MR | Zbl

[2] A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, Appl. Math. Sci., 120, Springer, New York, 2011 | MR | Zbl