Reconstruction of potential function in inverse Sturm-Liouville problem via partial data

Açil M., Konuralp A.

International Journal of Optimization and Control: Theories and Applications, vol.11, no.2, pp.186-198, 2021 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.11121/ijocta.01.2021.001090
  • Journal Name: International Journal of Optimization and Control: Theories and Applications
  • Journal Indexes: Scopus, Academic Search Premier, Communication Abstracts, zbMATH, Directory of Open Access Journals, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.186-198
  • Keywords: Numerical approximation of eigenvalues and of other parts of the spectrum, Optimization, Sturm-Liouville theory
  • Van Yüzüncü Yıl University Affiliated: Yes


© 2021 Balikesir University. All rights reserved.In this paper, three different uniqueness data are investigated to reconstruct the potential function in the Sturm-Liouville boundary value problem in the normal form. Taking account of Röhrl’s objective function, the steepest descent method is used in the computation of potential functions. To decrease the volume of computation, we propose a theorem to precalculate the minimization parameter that is required in the optimization. Further, we propose a novel time-saving algorithm in which the obligation of using the asymptotics of eigenvalues and eigenfunctions and the appropriateness of selected boundary conditions are also eliminated. As partial data, we take two spectra, the set of the jth elements of the infinite numbers of spectra obtained by changing boundary conditions in the problem, and one spectrum with the set of terminal velocities. In order to show the efficiency of the proposed method, numerical results are given for three test potentials which are smooth, nonsmooth continuous, and noncontinuous, respectively.