An efficient approximation for accelerating convergence of numerical power series: Results for the 1D-Schrödinger equation

Abstract

The numerical matrix Numerov algorithm is used to solve the stationary Schrödinger equation for central Coulomb potentials. An efficient approximation for accelerating its convergence is proposed. The Numerov method can lead to error if the dimension of grid-size is not chosen properly. A number of rules so far have been proposed. The effectiveness of these rules decreases for more complicated equations. Efficiency of the technique used for convergence acceleration is tested by allowing the grid-sizes to have variationally optimized values. The method presented in this study reduces effective increasing margin of error during the calculation for excited states. The results obtained for energy eigenvalues are compared with those found in the literature. It is observed that, once the values of grid-sizes for hydrogen energy eigenvalues are obtained, they can simply be employed for the hydrogen iso-electronic series as, hɛ(Z) = hɛ(1)/Z. © 2023 Elsevier Inc.