Computing the spectral function for singular Sturm--Liouville problems
Algorithms for computing Sturm-Liouville spectral density functions are developed based on several mathematical characterizations. Especially singular Sturm-Liouville problems of the form \[ -U''+q(x)U=\lambda U,\quad x\in [a,\infty) \] and \[ U(a)\cos\alpha +U'(a)\sin\alpha=0 \] are studied when \(q\) belongs to Weyl's limit point case and generates some continuous spectrum. Convergence and error bounds are derived and methods are tested on several examples. The results are compared with those from the existing software package SLEDGE.
scientific article; zbMATH DE number 2137367