Reconstructing the potential function and its derivatives using nodal data

Abstract

We solve the inverse nodal problem of reconstructing the potential function q and its derivatives, as well as the boundary conditions of a Sturm-Liouville problem using the nodal points together with the integral average of q. All the algorithms have a first-order convergence rate. They seem to be useful in studying the smoothness of the potential function. Our method is based on the works of Shen, and can also work for other similar inverse nodal problems.