A new four-step hybrid type method with vanished phase-lag and its first derivatives for each level for the approximate integration of the Schr?dinger equation

摘要

In this paper we present a new methodology for the development of four-step hybrid type methods of sixth algebraic order with vanished phase-lag and its derivatives. The methodology is based on the vanishing of the phase-lag and its derivatives on its level of the hybrid method. We present a comparative error and stability analysis for the produced new method. The efficiency of the new obtained methods is examined by application to the resonance problem of the Schr?dinger equation.