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<p>In this paper, the authors presented a numerical scheme and experiments for the inverse nodal problem for the Sturm-Liouville operator on star-shaped graphs. Additionally, we investigate the convergence analysis of the approximate solutions and provide error estimates. As an application of the numerical methods, we derive a new uniqueness theorem for the potentials of the Sturm-Liouville operator, based on parts of the nodal set and a constant. A novel aspect of this study is the application of numerical methods to this problem.</p>

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A Partial Inverse Nodal Problem for Sturm-Liouville Operators on Star-Shaped Graphs

  • 期刊论文

  • 发表日期：

    2026年2月5日

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  • Haoze Ni,
  • Chung-Tsun Shieh,
  • Tzong-Mo Tsai,
  • Yu Ping Wang

摘要

In this paper, the authors presented a numerical scheme and experiments for the inverse nodal problem for the Sturm-Liouville operator on star-shaped graphs. Additionally, we investigate the convergence analysis of the approximate solutions and provide error estimates. As an application of the numerical methods, we derive a new uniqueness theorem for the potentials of the Sturm-Liouville operator, based on parts of the nodal set and a constant. A novel aspect of this study is the application of numerical methods to this problem.