10.1007/s40096-023-00520-5

Solving inverse Sturm–Liouville problem featuring a constant delay by Chebyshev interpolation method

  • A. Dabbaghian1,
  • S. Akbarpoor Kiasary2,
  • H. Koyunbakan3,
  • B. Agheli*4,
  1. Department of Mathematics, Neka Branch, Islamic Azad University, Neka, IR
  2. Department of Mathematics, Jouybar Branch, Islamic Azad University, Jouybar, IR
  3. Department of Mathematics, Firat University, Elazig, 23119, TR
  4. Department of Mathematics, Qaemshar Branch, Islamic Azad University, Qaemshahr, IR

Published 2024-01-02

How to Cite

Dabbaghian, A., Kiasary, S. A., Koyunbakan, H., & Agheli, B. (2024). Solving inverse Sturm–Liouville problem featuring a constant delay by Chebyshev interpolation method. Mathematical Sciences, 18(4 (December 2024). https://doi.org/10.1007/s40096-023-00520-5
Crossref
Scopus
Google Scholar
Europe PMC

Abstract

Abstract The inverse nodal problem for Sturm–Liouville operator with a constant delay has been investigated in the present paper. To do so, we have computed the nodal points and nodal lengths. Therefore, we have tried Chebyshev interpolation technique (CIT) to obtain the numerical solution of inverse nodal problem. Following that, a number of numerical examples have been given. The numerical calculations in the present paper have been conducted via pc applying some programs encoded in Matlab software.

Keywords

  • Inverse problem (IP),
  • Sturm–Liouville (SL) operator,
  • Constant delay,
  • Chebyshev interpolation (CI)

References

  1. Mohammed et al. (2017) Periodicity computation of generalized mathematical biology problems involving delay differential equations 24(3) (pp. 737-740) https://doi.org/10.1016/j.sjbs.2017.01.050
  2. Jackson and Chen-Charpentier (2017) Modeling plant virus propagation with delays (pp. 611-621) https://doi.org/10.1016/j.cam.2016.04.024
  3. Shampine and Gahinet (2006) Delay-differential-algebraic equations in control theory 56(3–4) (pp. 574-588) https://doi.org/10.1016/j.apnum.2005.04.025
  4. Soltan Mohamadi et al. (2014) Periodic solutions of delay differential equations with feedback control for enterprise clusters based on ecology theory 2014(1) (pp. 1-15) https://doi.org/10.1186/1029-242X-2014-306
  5. Graef et al. (2002) Oscillation of impulsive neutral delay differential equations 268(1) (pp. 310-333) https://doi.org/10.1006/jmaa.2001.7836
  6. Duan et al. (2003) Oscillation and stability of nonlinear neutral impulsive delay differential equations 11(1) (pp. 243-253) https://doi.org/10.1007/BF02935734
  7. Milano and Dassios (2016) Small-signal stability analysis for non-index 1 Hessenberg form systems of delay differential-algebraic equations 63(9) (pp. 1521-1530) https://doi.org/10.1109/TCSI.2016.2570944
  8. Lenz et al. (2014) Numerical computation of derivatives in systems of delay differential equations (pp. 124-156) https://doi.org/10.1016/j.matcom.2013.08.003
  9. Levitan and Sargsjan (1975) American Mathematical Society https://doi.org/10.1090/mmono/039
  10. Lowe (1992) The recovery of potentials from finite spectral data 23(2) (pp. 482-504) https://doi.org/10.1137/0523023
  11. Hryniv and Pronska (2012) Inverse spectral problems for energy-dependent Sturm–Liouville equations 28(8)
  12. McLaughlin (1988) Inverse spectral theory using nodal points as data-a uniqueness result (pp. 342-362) https://doi.org/10.1016/0022-0396(88)90111-8
  13. Akbarpoor et al. (2019) Solving inverse nodal problem with spectral parameter in boundary conditions https://doi.org/10.1080/17415977.2019.1597871
  14. Browne and Sleeman (1996) Inverse nodal problem for Sturm–Liouville equation with eigenparameter dependent boundary conditions (pp. 377-381) https://doi.org/10.1088/0266-5611/12/4/002
  15. Freiling and Yurko (2001) NOVA Science Publishers
  16. Gulsen et al. (2018) Numerical investigation of the inverse nodal problem by Chebyshev interpolation method (pp. S123-S136) https://doi.org/10.2298/TSCI170612278G
  17. Koyunbakan and Panakhov (2007) A uniqueness theorem for inverse nodal problem (pp. 517-524)
  18. Law et al. (1999) The inverse nodal problem on the smoothness of the potential function (pp. 253-263)
  19. Neamaty et al. (2017) Solving inverse Sturm–Liouville problem with separated boundary conditions by using two different input data https://doi.org/10.1080/00207160.2017.1346244
  20. Neamaty et al. (2019) The numerical values of the nodal points for the Sturm–Liouville equation with one turning point 7(1) (pp. 124-137)
  21. Wang et al. (2017) IPs for the boundary value problem with the interior nodal subsets (pp. 1229-1239) https://doi.org/10.1080/00036811.2016.1183770
  22. Hale (1977) Springer https://doi.org/10.1007/978-1-4612-9892-2
  23. Myshkis (1972) Nauka
  24. Buterin et al. (2017) Sturm–Liouville differential operators with deviating argument 48(1) (pp. 61-71)
  25. Freiling and Yurko (2012) IPs for Sturm–Liouville differential operators with a constant delay (pp. 1999-2004) https://doi.org/10.1016/j.aml.2012.03.026
  26. Murat and Chung (2018) Inverse nodal problems for integro-differential operators with a constant delay https://doi.org/10.1515/jiip-2018-0088
  27. Wang et al. (2018) Reconstruction for Sturm–Liouville equations with a constant delay with twin-dense nodal subsets https://doi.org/10.1080/17415977.2018.1489803
  28. Yang (2014) Inverse nodal problems for the Sturm–Liouville operator with a constant delay (pp. 1288-1306) https://doi.org/10.1016/j.jde.2014.05.011
  29. Rashed (2003) Numerical solution of a special type of integro-differential equations (pp. 73-88)
  30. Rashed (2003) Numerical solutions of the integral equations of the first kind (pp. 413-420)
  31. Greenberg and Marletta (1998) Oscillation theory and numerical solution of sixth-order Sturm–Liouville problems 35(5) (pp. 2070-2098) https://doi.org/10.1137/S0036142997316451
  32. Mirzaei (2017) Computing the eigenvalues of fourth-order Sturm–Liouville problems with Lie group method 7(1) (pp. 1-12) https://doi.org/10.22067/ijnao.v7i1.44788
  33. Glsen and Panahkov (2018) On the isospectrality of the scalar energy-dependent Schroinger problems 42(1) (pp. 139-154) https://doi.org/10.3906/mat-1612-71
  34. Mirzaei (2018) A family of isospectral fourth-order Sturm–Liouville problems and equivalent beam equations 23(1) (pp. 15-27)
  35. Mirzaei (2020) Higher-order Sturm–Liouville problems with the Same eigenvalues (pp. 409-417) https://doi.org/10.3906/mat-1911-17
  36. Levitan, BM.: Inverse Sturm–Liouville Problems. VNU Science Press, (1987)
  37. Borg (1945) Eine umkehrung der Sturm–Liouvilleschen eigenwertaufgabe (pp. 1-96) https://doi.org/10.1007/BF02421600
  38. Shahriari (2014) Inverse Sturm–Liouville problems with transmission and spectral parameter boundary conditions 2(3) (pp. 123-139)
  39. Shahriari (2016) Inverse Sturm–Liouville problems with a spectral parameter in the boundary and transmission condition 3(2) (pp. 75-89)
  40. Shahriari et al. (2012) Uniqueness for inverse Sturm–Liouville problems with a finite number of transmission conditions (pp. 19-29) https://doi.org/10.1016/j.jmaa.2012.04.048
  41. Teschl (2009) Amer. Math. Soc
  42. Sadek et al. (2023) A numerical approach based on Bernstein collocation method: Application to differential Lyapunov and Sylvester matrix equations (pp. 475-488) https://doi.org/10.1016/j.matcom.2023.05.011
  43. Sadek et al. (2023) The novel Mittag-Leffler-Galerkin method: application to a Riccati differential equation of fractional order 7(4) https://doi.org/10.3390/fractalfract7040302
  44. Dascioglu and Isle (2013) Bernstein collocation method for solving nonlinear differential equations 18(3) (pp. 293-300)