Inverse Nodal Problem for the Sturm-Liouville Operator with Three Discontinuities

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Abstract

In this work, the inverse nodal problem for the Sturm-Liouville operator with three discontinuities is studied. It is proved that the dense nodes of the eigenfunctions can uniquely determine the potential on the whole interval and some parameters, and a reconstruction algorithm for the solution is presented. Finally, numerical examples were provided, and the effectiveness of the algorithm was verified through numerical calculations.

Keywords:

Inverse nodal problems Discontinuities Uniqueness theorem Reconstruction algorithm

Author Biographies

  • Ran Zhang

    School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

    School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China

  • Xin-Jian Xu

    School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China

  • Chuan-Fu Yang

    School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China

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DOI

10.4208/jcm.2510-m2025-0196

How to Cite

Inverse Nodal Problem for the Sturm-Liouville Operator with Three Discontinuities. (2025). Journal of Computational Mathematics. https://doi.org/10.4208/jcm.2510-m2025-0196