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Solving inverse nodal problems of Sturm–Liouville operator with a point interaction based on Legendre wavelet bases

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  • Jiang, Chen-Tian
  • Xu, Xin-Jian
  • Yang, Chuan-Fu

Abstract

This paper investigates a numerical method for solving inverse nodal problems of Sturm–Liouville operator with a point interaction based on Legendre wavelet bases, reconstructing the potential function and the strength of point interactions from the nodal data of a single eigenfunction. Firstly, the previous results on the asymptotic estimates of eigenvalues and nodal points of this operator are stated. Secondly, a modified uniqueness theorem is established to characterize determination of the potential function and the strength of a point interaction from the nodal data. Finally, numerical experiments are conducted to reconstruct the potential function and the strength of a point interaction using Legendre wavelet bases and a finite set of nodal data. The numerical results demonstrate that, under the same nodal data, the Legendre wavelet-based algorithm significantly outperforms traditional methods, which achieves higher accuracy in fitting the potential function and the strength of a point interaction compared to algorithms based on polynomial or trigonometric bases.

Suggested Citation

  • Jiang, Chen-Tian & Xu, Xin-Jian & Yang, Chuan-Fu, 2026. "Solving inverse nodal problems of Sturm–Liouville operator with a point interaction based on Legendre wavelet bases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 250(C), pages 1313-1324.
    • Handle: RePEc:eee:matcom:v:250:y:2026:i:c:p:1313-1324
    DOI: 10.1016/j.matcom.2026.07.019
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