Convergence of Numerov’s method for inverse Sturm–Liouville problems

In this paper, we discuss the convergence of Numerov’s method in Andrew (2005, 2006) [8,9] for computing Sturm–Liouville potentials from the given eigenvalues. By using the asymptotic estimate for the eigenvalue of the Sturm–Liouville problem and the error in the finite difference eigenvalue, convergence of Numerov’s method for symmetric potentials is proved. Based on the method of symmetric extension, we establish a convergence result of Numerov’s method for the nonsymmetric potential from two spectra. Numerical examples are reported to confirm the theoretically predicted convergence.