New embedded explicit methods with minimal phase-lag for the numerical integration of the Schrödinger equation

Abstract

A new family of explicit two-step Numerov-type methods with minimal phase-lag is developed for the numerical integration of the Schrödinger equation. Based on this family of methods and on the phase-lag error-control procedure, an embedded method is developed. An application to the phase shift problem of the radial Schrödinger equation and to the coupled differential equations arising from the Schrödinger equation, indicates that these new methods are generally more efficient than other previously developed finite difference methods.