Boundary value method for inverse Sturm-Liouville problems

In this paper we present a method to recover symmetric and non-symmetric potential functions of inverse Sturm-Liouville problems from the knowledge of eigenvalues. The linear multistep method coupled with suitable boundary conditions known as boundary value method (BVM) is the main tool to approximate the eigenvalues in each iteration step of the used Newton method. The BVM was extended to work for Neumann-Neumann boundary conditions. Moreover, a suitable approximation for the asymptotic correction of the eigenvalues is given. Numerical results demonstrate that the method is able to give good results for both symmetric and non-symmetric potentials.