An explicit eighth-order method with minimal phase-lag for accurate computations of eigenvalues, resonances and phase shifts

Abstract

A new explicit hybrid eighth algebraic order two-step method with phase-lag of order ten is developed for computing eigenvalues, resonances and phase shifts of the one-dimensional Schrödinger equation and coupled differential equations arising from the Schrödinger equation. Based on this new method and on the method developed recently by Simos we obtain a new variable-step procedure for the numerical integration of the Schrödinger equation. Numerical results obtained for the integration of the resonance problem for the well known case of the Woods-Saxon potential, for the integration of the eigenvalue problem for the well known case of the Morse potential and for the integration of coupled differential equations show that this new method is better than other variable-step methods.