High-order methods with minimal phase-lag for the numerical integration of the special second-order initial value problem and their application to the one-dimensional Schrödinger equation

Abstract

Two two-step sixth-order methods with phase-lag of order eight and ten are developed for the numerical integration of the special second-order initial value problem. One of these methods is P-stable and the other has an interval of periodicity larger than the Numerov method. An application to the one-dimensional Schrödinger equation on the resonance problem, indicates that these new methods are generally more accurate than methods developed by Chawla and Rao. We note that the new methods introduce a new approach for the numerical integration of the Schrödinger equation.