Numerical Approaches to the Inverse Nodal Problem for Diffusion Operators on Star Graphs with Nonhomogeneous Edges

This paper presents numerical approaches to the inverse nodal problem for a diffusion operator defined on a star graph with nonhomogeneous edges. Based on the asymptotic behavior of sufficiently large eigenvalues, nodal data are employed to reconstruct the potential functions and the parameters appearing in the boundary conditions. The numerical analysis is carried out separately for odd and even star graph configurations, with distinct treatments on the subintervals and . This interval-based strategy enables an effective investigation of the influence of graph parity and edge nonhomogeneity on the inverse reconstruction process. Several numerical examples are provided to illustrate the accuracy and efficiency of the proposed methods.