SavedAdd your journal

Journals / Turkish Journal of Mathematics and Computer Science / 2025 / Volume: 17 Issue: 2

Solving Symmetric Inverse Sturm-Liouville Problem for Neumann Boundary Conditions

İbrahim Adalar(SIVAS CUMHURIYET UNIVERSITY)0000-0002-4224-0972
Pages
—
Publication Date
2025-12-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We give an algorithm for the reconstruction of the symmetric potential of problem using a special coefficient matrix.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present paper, we consider the inverse Sturm-Liouville problem with Neumann boundary conditions.
📊
Key Findings & Data:In the present paper, we consider the inverse Sturm-Liouville problem with Neumann boundary conditions.
💡
Conclusion & Impact:We give an algorithm for the reconstruction of the symmetric potential of problem using a special coefficient matrix.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Inverse Problem · Sturm-Liouville Equation · Neumann Boundary Conditions

Abstract

In the present paper, we consider the inverse Sturm-Liouville problem with Neumann boundary conditions. We give an algorithm for the reconstruction of the symmetric potential of problem using a special coefficient matrix.

🔖

Cite This Article

Adalar, İ. (2025). Solving Symmetric Inverse Sturm-Liouville Problem for Neumann Boundary Conditions. Turkish Journal of Mathematics and Computer Science, Volume: 17 Issue: 2. https://doi.org/10.47000/tjmcs.1672430

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (33)

  1. Aceto, L., Ghelardoni, P., Magherini, C., Boundary value methods for the reconstruction of Sturm–Liouville potentials, App. Math. Comp., 6(2012), 2960–2974.
  2. Ambarzumian, V.A., Ueber eine frage der eigenwerttheorie, Z. Phys., (1929), 690–695.
  3. Andrew, A.L., Asymptotic correction of Numerov’s eigenvalue estimates with natural boundary conditions, J.Comp.Appl.Math., 125(1-2)(2000), 359–366.
  4. Andrew, A.L., Computing Sturm–Liouville potentials from two spectra, Acta Math., 22(2006), 2069–2081.
  5. Bondarenko, N.P., Finite-difference approximation of the inverse Sturm–Liouville problem with frozen argument, App. Math. Comp., 413(2022), 126653.
  6. Borg, G., Eine umkehrung der Sturm-Liouvilleschen eigenwertaufgabe, Acta Math., 78(1946), 1–96.
  7. Buterin, S.A., On the reconstruction of a convolution perturbation of the Sturm-Liouville operator from the spectrum, Dif. Equ., 46(1)(2010), 150–154.
  8. Fabiano, R.H., Knobel, R., Lowe, B.D., A finite-difference algorithm for an inverse Sturm-Liouville problem, IMA journal of numerical analysis, 15(1)(1995), 75–88.
  9. Freiling, G., Yurko, V.A., Inverse Sturm-Liouville Problems and Their Applications, NOVA Science Publishers, Huntington, 2001.
  10. Gao, Q., Cheng, X., Huang, Z., Modified Numerov’s method for inverse Sturm-Liouville problems, Journal of computational and applied mathematics, 253(2013), 181–199.
  11. Hald, O.H., The inverse Sturm-Liouville problem and the Rayleigh-Ritz method, Math. Comp., 32(143) (1978), 687–705.
  12. Hochstadt, H., Lieberman, B., An inverse Sturm–Liouville problem with mixed given data, SIAM J. App. Math., 34(4)(1978), 676–680.
  13. Ignatiev, M., Yurko, V., Numerical methods for solving inverse Sturm–Liouville problems,Results in Math., 52(1)(2008), 63–74.
  14. Jiang, X., Li, X., Xu, X., Numerical algorithms for inverse Sturm-Liouville problems, Numerical Algorithms, 89(3)(2022), 1287–1309.
  15. Kammanee, A., B¨ockmann, C., Boundary value method for inverse Sturm–Liouville problems, App. Math. Comp., 214(2)(2009), 342–352.
  16. Kravchenko, V.V., Direct and Inverse Sturm-Liouville Problems, Birkh¨auser, Cham, 2020.
  17. Kravchenko, V.V., Torba, S.M., A direct method for solving inverse Sturm-Liouville problems, J. Diff. Eq., 37(1)(2020), 015015.
  18. Kravchenko, V.V., Spectrum completion and inverse Sturm-Liouville problems, Math. Meth. Appl. Sci., 46(5)(2023), 5821–5835.
  19. Levinson, N., The inverse Sturm-Liouville problem, Math. Tidsskr. B., 13(1949), 25–30.
  20. Liu, C.S., Li, B., Solving Sturm–Liouville inverse problems by an orthogonalized enhanced boundary function method and a product formula for symmetric potential, Mathematics and Computers in Simulation, 210(2023), 640–660.
  21. Liu, C.S., Li, B., The eigenvalues of symmetric Sturm-Liouville problem and inverse potential problem, based on special matrix and product formula, Applications of Mathematics, 69(3)(2024), 355–372.
  22. Lowe, B.D., Pilant, M., Rundell, W., The recovery of potentials from finite spectral data, SIAM J. Math. Analysis, 23(2)(1992), 482–504.
  23. McLaughlin, J.R., Inverse spectral theory using nodal points as data - a uniqueness result, J. Diff. Eq., 69(73)(1988), 354–362.
  24. Neamaty, A., Akbarpoor, S., Yılmaz, E., Solving symmetric inverse Sturm–Liouville problem using Chebyshev polynomials, Mediterranean Journal of Mathematics, 16(2019), 1–17.
  25. Perera, U., B¨ockmann, C.,Solutions of Sturm-Liouville problems, Mathematics, 8(11)(2020), 2074.
  26. Plum, M. Eigenvalue inclusions for second-order ordinary differential operators by a numerical homotopy method, Zeitschrift f¨ur angewandte Mathematik und Physik ZAMP, 41(2)(1990), 205–226.
  27. Röhrl, N., A least-squares functional for solving inverse Sturm–Liouville problems, Inverse Probl. 21(2005), 2009–2017.
  28. Rundell, W., Sacks, P.E., Reconstruction techniques for classical inverse Sturm-Liouville problems, Mathematics of Computation, 58(197)(1992), 161–183.
  29. Rundell, W., Sacks, P.E., The reconstruction of Sturm-Liouville operators, Inverse problems, 8(3)(1992), 457–482
  30. Sacks, P.E., An iterative method for the inverse Dirichlet problem, Mathematics of Computation, 4(4)(1988), 1055.
  31. Shahriari, M., Akbarfam, A.J., Teschl, G., Uniqueness for inverse Sturm–Liouville problems with a finite number of transmission conditions, J. Math. Anal. Appl., 395(1)(2012), 19–29.
  32. Fabiano, R.H., Knobel, R., Lowe, B.D., A finite-difference algorithm for an inverse Sturm-Liouville problem, IMA journal of numerical analysis, 15(1)(1995), 75–88.
  33. Kravchenko, V.V., Spectrum completion and inverse Sturm-Liouville problems, Math. Meth. Appl. Sci., 46(5)(2023), 5821–5835.