A Numerical Method for the Inverse Sturm–Liouville Problem

In this paper we present a method for solving a form of the inverse Sturm–Liouville problem. The basis of the method is to modify the given differential eigenvalues so that the N × N tridiagonal matrix eigenvalue problem recovered from the first N eigenvalues can (after a suitable transformation) be identified with the finite difference approximation of the required differential eigenvalue problem. Numerical results are presented to illustrate the effectiveness of this method.