An algorithm for discontinuous inverse Sturm-Liouville problems with symmetric potentials

Abstract

In this paper we consider two Sturm-Liouville problems with symmetric potentials and symmetric discontinuities satisfying symmetric boundary and jump conditions. In the first section we derive a simple expression for the difference of potentials when only a finite number of eigenvalues differ. In the second section this result is used to construct an algorithm for solving the discontinuous inverse Sturm-Liouville problem numerically. © 1989.