Solving a nonlinear inverse Sturm–Liouville problem with nonlinear convective term using a boundary functional method

References

• Gelfand IM, Levitan BM. On the determination of a differential equation from its spectral function. Amer Math Soc Transl. 1951;1:253–304.
   Google Scholar
• McLaughlin JR. Analytical methods for recovering coefficients in differential equations from spectral data. SIAM Rev. 1986;28:53–72. doi: 10.1137/1028003
   Web of Science ®Google Scholar
• Bondarenko NP, Buterin SA, Vasiliev SV. An inverse spectral problem for Sturm–Liouville operators with frozen argument. J Math Anal Appl. 2019;472:1028–1041. doi: 10.1016/j.jmaa.2018.11.062
   Web of Science ®Google Scholar
• Sat M, Panakhov ES. A uniqueness theorem for Bessel operator from interior spectral data. Abstr Appl Anal. 2013; ID 713654.
   Google Scholar
• Chu MT. Inverse eigenvalue problems. SIAM Rev. 1998;40:1–39. doi: 10.1137/S0036144596303984
   Web of Science ®Google Scholar
• Andrew AL. Numerical solution of inverse Sturm–Liouville problems. ANZIAM J. 2004;45E:C326–C337. doi: 10.21914/anziamj.v45i0.891
   Google Scholar
• Paine J. A numerical method for the inverse Sturm–Liouville problem. SIAM Sci Stat Comput. 1984;5:149–156. doi: 10.1137/0905011
   Web of Science ®Google Scholar
• McLaughlin JR. Inverse spectral theory using nodal points as data–a uniqueness result. J Differ Equ. 1988;73:354–362. doi: 10.1016/0022-0396(88)90111-8
   Web of Science ®Google Scholar
• Browne PJ, Sleeman BD. Inverse nodal problem for Sturm-Liouville equation with eigenparameter depend boundary conditions. Inverse Probl. 1996;12:377–381. doi: 10.1088/0266-5611/12/4/002
   Web of Science ®Google Scholar
• Cheng YH, Law CK, Tsay J. Remarks on a new inverse nodal problem. J Math Anal Appl. 2000;248:145–155. doi: 10.1006/jmaa.2000.6878
   Web of Science ®Google Scholar
• Hald O, McLaughlin JR. Solutions of inverse nodal problems. Inverse Probl. 1989;5:307–347. doi: 10.1088/0266-5611/5/3/008
   Web of Science ®Google Scholar
• Yang FX. A solution of the inverse nodal problem. Inverse Probl. 1997;13:203–213. doi: 10.1088/0266-5611/13/1/016
   Web of Science ®Google Scholar
• Sat M, Shieh CT. Inverse nodal problems for integro-differential operators with a constant delay. J Inverse Ill-posed Probl. 2019;27:501–509. doi: 10.1515/jiip-2018-0088
   Web of Science ®Google Scholar
• Boley D, Golub GH. A survey of matrix inverse eigenvalue problems. Inverse Probl. 1987;3:595–622. doi: 10.1088/0266-5611/3/4/010
   Web of Science ®Google Scholar
• Liu CS. Solving an inverse Sturm–Liouville problem by a Lie-group method. Boundary Value Problems. 2008; Article ID 749865.
   Web of Science ®Google Scholar
• Liu CS, Atluri SN. A novel fictitious time integration method for solving the discretized inverse Sturm–Liouville problems, for specified eigenvalues. Comput Model Eng Sci. 2008;36:261–285.
   Web of Science ®Google Scholar
• Hasanov A, Shores TS. Solution of an inverse coefficient problem for an ordinary differential equation. Appl Anal. 1997;67:11–20. doi: 10.1080/00036819708840594
   Google Scholar
• Kaltenbacher B. A projection-regularized Newton method for nonlinear ill-posed problems and its application to parameter identification problems with finite element discretization. SIAM J Numer Anal. 2000;37:1885–1908. doi: 10.1137/S0036142998347322
   Web of Science ®Google Scholar
• Hasanov A, Pektas B. Simulation of ill-conditioned situations in inverse coefficient problem for the Sturm–Liouville operator based on boundary measurements. Math Comput Simul. 2002;61:47–52. doi: 10.1016/S0378-4754(02)00134-9
   Web of Science ®Google Scholar
• Hasanov A. An inverse polynomial method for the identification of the leading coefficient in the Sturm–Liouville operator from boundary measurements. Appl Math Comput. 2003;140:501–515.
   Web of Science ®Google Scholar
• Liu CS. An inverse problem for computing a leading coefficient in the Sturm–Liouville operator by using the boundary data. Appl Math Comput. 2011;218:4245–4259.
   Web of Science ®Google Scholar
• Liu CS. Identifying a rigidity function distributed in static composite beam by the boundary functional method. Compos Struct. 2017;176:996–1004. doi: 10.1016/j.compstruct.2017.06.003
   Web of Science ®Google Scholar
• Liu CS, Li B. Reconstructing a second-order Sturm–Liouville operator by an energetic boundary function iterative method. Appl Math Lett. 2017;73:49–55. doi: 10.1016/j.aml.2017.04.023
   Web of Science ®Google Scholar