On A Modified Numerov'S Method For Inverse Sturm-Liouville Problems

In this paper, we discuss the convergence of modified Numerov's method in Q. Gao, X.L. Cheng and Z.D. Huang [Modified Numerov's method for inverse Sturm-Liouville problems, J. Comput. Appl. Math. 253 (2013), pp. 181-199] for computing symmetric potentials from finite Dirichlet eigenvalues. A sufficient condition for convergence of the estimate to the true potential is given and the rate of convergence is investigated. The proof relies on the asymptotics of eigenvalues of the Sturm-Liouville operator and the errors in the finite difference eigenvalues obtained by Numerov's approach. Some numerical experiments are presented to confirm the theoretically predicted convergence properties.