Decent flow methods for inverse Sturm–Liouville problem

In this paper, we propose three numerical methods for the inverse Sturm–Liouville operator in impedance form. We use a finite difference method to discretize the Sturm–Liouville operator and expand the impedance function with some basis functions. The correction technique is discussed. By solving an un-weighted least squares problem, we find an approximation to the impedance function. Numerical experiments are presented to show the accuracy and stability of the numerical methods.