A Generalization of Numerov's Method Using the BVM Approach for Sturm-Liouville Eigenvalue estimates

Boundary Value Methods generalizing the Numerov's method are here proposed for the numerical approximation of the eigenvalues of regular Sturm-Liouville problems subject to Dirichlet boundary conditions. Moreover, an analysis of the error in the approximation of the k-th eigenvalue provided by such methods is reported. Some numerical results showing the possible advantages that may arise from the use of the new schemes are also presented.