Numerov-type methods with minimal phase-lag for the numerical integration of the one-dimensional Schrödinger equation

Abstract

Three Numerov-type methods with phase-lag of order eight and ten are developed for the numerical integration of the one-dimensional Schrodinger equation. One has a large interval of periodicity and the other two areP-stable. Extensive numerical testing on the resonance problem indicates that these new methods are generally more accurate than other previously developed finite difference methods for this problem.