ON THE ESTIMATIONS OF THE SMALL EIGENVALUES OF NON-SELF-ADJOINT STURM-LIOUVILLE OPERATORS

Year 2019, Volume: 9 Issue: 4, 1 - 12, 01.12.2019

C. Nur O. A. Veliev

Abstract

We give a new approach for the estimations of the eigenvalues of non-selfadjoint Sturm-Liouville operators with regular but not strongly regular boundary conditions. Moreover we give the error estimations.

Keywords

Eigenvalue estimations, Regular boundary conditions, Numerical methods, Sturm-Liouville Operators.

References

• Annaby, M. H. and Asharabi, R. H., (2008), On sinc-based method in computing eigenvalues of boundary-value problems, SIAM J. Numer. Anal., 46, pp. 671-690.
• Annaby, M. H. and Asharabi, R. H., (2012), Computing eigenvalues of Sturm-Liouville problems by Hermite interpolations, Numer. Algorithms, 60 (3), pp. 355-367.
• Boumenir, A., (2001), Sampling and eigenvalues of non-self-adjoint Sturm–Liouville problems, SIAM J. Sci. Comput., 23, pp. 219-229.
• Chanane, B., (1999), Computing eigenvalues of regular Sturm-Liouville problems, Appl. Math. Lett., 12, pp. 119-125.
• Dinib¨ut¨un, S. and Veliev, O. A., (2013), On the Estimations of the Small Periodic Eigenvalues, Abstract and Applied Analysis, Article ID: 145967.
• Goh, C. J., Teo, K. L. and Agarwal, R. P., (1994), Computing Eigenvalues of Sturm-Liouville Problems via Optimal Control Theory, Mathl. Comput. Modelling, 19 (10), pp. 1-10.
• Malathi, V., Suleiman, M. B. and Taib, B. B., (1998), Computing eigenvalues of periodic Sturm- Liouville problems using shooting technique and direct integration method, International Journal of Computer Mathematics, 68 (1-2), pp. 119-132.
• Nur, C. and Veliev, O. A., (2014), On the basis property of the root functions of some class of non-self-adjoint Sturm-Liouville operators, Boundary Value Problems, 2014:57.
• Shkalikov, A. A., (1982), On the basis property of the eigenfunctions of ordinary differential operators with integral boundary conditions, Vestnik Moscow University, Ser. Mat. Mekh., 37 (6), pp. 12-21