Work

Numerical Methods for Partial Inverse Spectral Problems with Frozen Arguments on Star-Shaped Graphs

Year: 2025

Type: article

Abstract: In this paper, the authors investigate a partial inverse spectral problem for Sturm–Liouville operators with frozen arguments on star-shaped graphs. The problem is to reconstruct the potential on one edge from the known potentials on the other edges together with two sequences of eigenvalues from a prescribed spectral set. The proposed approach is constructive. First, the characteristic function associated with the given spectral data is constructed, allowing the unknown potential contribution to be isolated. The potential is then recovered by expanding the resulting expressions in an appropriate Riesz basis and solving a corresponding system of linear equations. Based on established uniqueness results, this procedure yields a constructive numerical algorithm. Numerical examples demonstrate reliable reconstruction for both smooth and piecewise continuous potentials, providing a practical scheme for frozen-argument problems on star graphs.

Source: Mathematics

DOI: 10.3390/math14010156

Authors: Chung-Tsun Shieh, Tzong-Mo Tsai, Jyh-Shyang Wu

Institutions: Tamkang University, Ming Chi University of Technology

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: National Science and Technology Council, National Science and Technology Council