An estimation of the eigenfunctions of periodic Sturm-Liouville problems

References

• Al-Gwaiz, M. A. (2008). Sturm-Liouville theory and its applications. London: Springer.
   Google Scholar
• Andrew, A. L. (1988). Correction of finite element eigenvalues for problems with natural or periodic boundary conditions. BIT Numerical Mathematics, 28(2), 254–269. doi:https://doi.org/10.1007/BF01934090
   Google Scholar
• Andrew, A. L. (1989). Correction of finite difference eigenvalues of periodic Sturm-Liouville problems. The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 30(4), 460–469. doi:https://doi.org/10.1017/S0334270000006391
   Google Scholar
• Ao, J-j., & Wang, J. (2019). Eigenvalues of Sturm-Liouville problems with distribution potentials on time scales. Quaestiones Mathematicae, 42(9), 1185–1197. doi:https://doi.org/10.2989/16073606.2018.1509394
   Web of Science ®Google Scholar
• Burden, R. L. (2001). Numerical analysis (7th ed.). Pacific Grove, CA: Brooks/Cole.
   Google Scholar
• Celik, I., & Gokmen, G. (2005). Approximate solution of periodic Sturm-Liouville problems with Chebysev collocation method. Applied Mathematics and Computation, 170(1), 285–295. doi:https://doi.org/10.1016/j.amc.2004.11.038
   Web of Science ®Google Scholar
• Condon, D. J. (1999). Corrected finite difference eigenvalues of periodic Sturm-Liouville problems. Applied Numerical Mathematics, 30(4), 393–401. doi:https://doi.org/10.1016/S0168-9274(98)00093-2
   Web of Science ®Google Scholar
• Dinibutun, S., & Veliev, O. A. (2013). On the estimations of the small periodic eigenvalues. Abstract and Applied Analysis, 2013, 1–11. doi:https://doi.org/10.1155/2013/145967
   Google Scholar
• Eastham, M. S. P. (1973). The spectral theory of periodic differential equations. Edinburgh: Scottish Academic Press.
   Google Scholar
• Gao, C., Li, X., & Zhang, F. (2018). Eigenvalues of discrete Sturm-Liouville problems with nonlinear eigenparameter dependent boundary conditions. Quaestiones Mathematicae, 41(6), 773–797. doi:https://doi.org/10.2989/16073606.2017.1401014
   Web of Science ®Google Scholar
• Ghelardoni, P. (1997). Approximations of Sturm-Liouville eigenvalues using boundary value methods. Applied Numerical Mathematics, 23(3), 311–325. doi:https://doi.org/10.1016/S0168-9274(96)00073-6
   Web of Science ®Google Scholar
• Hei, D., & Zheng, M. (2020). Investigation on the dynamic behaviors of a rod fastening rotor based on an analytical solution of the oil film force of the supporting bearing. Journal of Low Frequency Noise, Vibration and Active Control. doi:https://doi.org/10.1177/1461348420912857
   Google Scholar
• Ji, X. Z. (1994). On a shooting algorithm for Sturm-Liouville eigenvalue problems with periodic and semi-periodic boundary conditions. Journal of Computational Physics, 111(1), 74–80. doi:https://doi.org/10.1006/jcph.1994.1045
   Web of Science ®Google Scholar
• Ji, X., & Wong, Y. S. (1991). Prufer method for periodic and semiperiodic Sturm-Liouville eigenvalue problems. International Journal of Computer Mathematics, 39, 109–123.
   Web of Science ®Google Scholar
• Kutsenko, A. A., Shuvalov, A. L., Poncelet, O., & Norris, A.N. (2013). Spectral properties of a 2D scalar wave equation with 1D periodic coefficients: Application to shear horizontal elastic waves. Mathematics and Mechanics of Solids, 18(7), 677–700. doi:https://doi.org/10.1177/1081286512444750
   Web of Science ®Google Scholar
• Liu, C. S. (2008). A Lie-group shooting method for computing eigenvalues and eigenfunctions of Sturm-Liouville problems. Computer Modeling in Engineering and Sciences, 26(3), 157–168.
   Web of Science ®Google Scholar
• Malathi, V., Suleiman, M. B., & 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), 119–132. doi:https://doi.org/10.1080/00207169808804682
   Web of Science ®Google Scholar
• Mukhtarov, O., & Yucel, M. (2020). A study of the eigenfunctions of the Singular Sturm–Liouville problem using the analytical method and the decomposition technique. Mathematics, 8(3), 415. doi:https://doi.org/10.3390/math8030415
   Web of Science ®Google Scholar
• Pryce, J. D. (1993). Numerical solution of Sturm-Liouville problems. Oxford: Oxford University Press.
   Google Scholar
• Vanden Berghe, G., Van Daele, M., & De Meyer, H. (1995). A modified difference scheme for periodic and semiperiodic Sturm–Liouville problems. Applied Numerical Mathematics, 18(1–3), 69–78. doi:https://doi.org/10.1016/0168-9274(95)00067-5
   Web of Science ®Google Scholar
• Wang, H., Zhao, L., & Hu, M. (2017). Eigenvalues of Sturm-Liouville problems with discontinuous boundary conditions. International Journal of Differential Equations, 2017(127), 1–27. doi:https://doi.org/10.1155/2017/2495686
   Google Scholar
• Yuan, Y., Sun, J., & Zettl, A. (2017). Eigenvalues of periodic Sturm Liouville problems. Linear Algebra and Its Applications, 517, 148–166. doi:https://doi.org/10.1016/j.laa.2016.11.035
   Web of Science ®Google Scholar
• Yucel, U. (2015). Numerical approximations of Sturm–Liouville eigenvalues using Chebyshev polynomial expansions method. Cogent Mathematics, 2(1).
   Google Scholar