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فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

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Khalili, Yasser, Dehghan, Mohammad. (1404). Computing high-index eigenvalues for the Sturm-Liouville equation with Robin boundary conditions. سامانه مدیریت نشریات علمی, 13(4), 1376-1384. doi: 10.22034/cmde.2024.60228.2566
Yasser Khalili; Mohammad Dehghan. "Computing high-index eigenvalues for the Sturm-Liouville equation with Robin boundary conditions". سامانه مدیریت نشریات علمی, 13, 4, 1404, 1376-1384. doi: 10.22034/cmde.2024.60228.2566
Khalili, Yasser, Dehghan, Mohammad. (1404). 'Computing high-index eigenvalues for the Sturm-Liouville equation with Robin boundary conditions', سامانه مدیریت نشریات علمی, 13(4), pp. 1376-1384. doi: 10.22034/cmde.2024.60228.2566
Khalili, Yasser, Dehghan, Mohammad. Computing high-index eigenvalues for the Sturm-Liouville equation with Robin boundary conditions. سامانه مدیریت نشریات علمی, 1404; 13(4): 1376-1384. doi: 10.22034/cmde.2024.60228.2566

Computing high-index eigenvalues for the Sturm-Liouville equation with Robin boundary conditions

Computational Methods for Differential Equations
مقاله 21، دوره 13، شماره 4، دی 2025، صفحه 1376-1384    اصل مقاله (397.04 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.60228.2566
نویسندگان
Yasser Khalili* 1؛ Mohammad Dehghan2
1Department of Basic Sciences‎, ‎Sari Agricultural Sciences and Natural Resources University‎, ‎578 Sari‎, ‎Iran.
2Department of Mathematics‎, ‎Sari Branch‎, ‎Islamic Azad University‎, ‎Sari‎, ‎Iran.
چکیده
The calculation of the high-indexed eigenvalues of Sturm-Liouville problems tends to be a complex job. The larger the eigenvalues are estimated, the greater the scaled errors we gain. In this paper, we study the Sturm-Liouville problems subject to Rubin boundary conditions in which the high-indexed eigenvalues are computed by means of an efficient method. In contrast to previous methods, the estimated errors of further eigenvalues are less than the primary ones. A good illustration of the accuracy of our method can be delineated by some numerical examples.
کلیدواژه‌ها
Sturm-Liouville operator؛ Robin boundary condition؛ High-index eigenvalue؛ Quadrature method
مراجع
  • [1] S. Abbasbandy and A. Shirzadi, A new application of the homotopy analysis method: Solving the Sturm-Liouville problems, Commun Nonlinear Sci Numer Simulat, 16 (2011), 112–126.
  • [2] L. Aceto, P. Ghelardoni, and C. Magherini, Boundary Value Methods as an extension of Numerovs method for Sturm-Liouville eigenvalue estimates, Applied Numerical Mathematics, 59 (2009), 1644–1656.
  • [3] M. Dehghan, An efficient method to approximate eigenfunctions and high-index eigenvalues of regular SturmLiouville problems, Applied Mathematics and Computation, 279 (2016), 249–257.
  • [4] G. Freiling and V. A. Yurko, Inverse Sturm-Liouville Problems and their Applications, NOVA Science Publ., New York, 2001.
  • [5] P. Ghelardoni, Approximations of Sturm-Liouville eigenvalues using Boundary Value Methods, Applied Numerical Mathematics, 23 (1997), 311–325.
  • [6] I. A. H. Hassan, On solving some eigenvalue problems by using a differential transformation, Applied Mathematics and Computation, 127(1) (2002), 1–22.
  • [7] A. Iserles and S. P. Norsett, Efficient quadrature of highly oscillatory integrals using derivatives, Proc. R. Soc. A, 461 (2005), 1383–1399.
  • [8] M. Jarratt, J. Lund, and K. L. Bowers, Galerkin schemes and the Sinc-Galerkin method for singular Sturm-Liouville problems, J. Computational Physics, 89(1) (1990), 41–62.
  • [9] V. Ledoux, M. Van Daele, and G. Vanden Berghe, Matslise: A Matlab package for the numerical solution of Sturm-Liouville and Schrodinger equations, ACM Transactions on Mathematical Software, 31 (2005), 532–554.
  • [10] J. D. Pryce, Classical and vector Sturm-Liouville problems: recent advances in singular-point analysis and shooting-type algorithms, J. Computational and Applied Mathematics, 50(1-3) (1994), 455–470.
  • [11] J. D. Pryce, Numerical Solution of Sturm-Liouville Problems, Oxford University Press, 1993.
  • [12] A. H. S. Taher and A. Malek, An efficient algorithm for solving high-order Sturm-Liouville problems using variational iteration method, Fixed Point Theory, 14 (2013), 193–210.
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