New variable-step algorithms for computing eigenvalues of the one-dimensional Schrödinger equation (Q1271719)

Two variable-step algorithms have been developed for computing eigenvalues of the radial Schrödinger equation. The eigenvalues are computed directly as roots of a function known in transmission line theory as the impendance. The novel numerical algorithms are based also on the piecewise perturbation analysis. The first new variable-step method is based on two methods, one with zeroth-order solution and the other with first-order perturbative corrections. The second method called `` block method'' is based on three methods, one with zeroth-order solution, another with first-order perturbative corrections and another with second-order perturbative corrections. Numerical results presented indicate the efficiency of the new variable-step methods.