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

Abstract

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

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

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.

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

Details

Primary Language English
Journal Section Research Article
Authors

C. NUR This is me
Department of Electrical and Electronics Engineering, Yalova University, Yalova, Turkey


O. A. VELİEV This is me
Department of Mathematics, Dogus University, Kadikoy, Istanbul, Turkey.

Publication Date December 1, 2019
Published in Issue Year 2019, Volume 9, Issue 4

Cite

Bibtex @ { twmsjaem760961, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2019}, volume = {9}, number = {4}, pages = {1 - 12}, title = {ON THE ESTIMATIONS OF THE SMALL EIGENVALUES OF NON-SELF-ADJOINT STURM-LIOUVILLE OPERATORS}, key = {cite}, author = {Nur, C. and Veliev, O. A.} }