Four-Step Hybrid type Methods with Vanished Phase-Lag and its Derivatives for Each Level for the Numerical Solution of the Schrodinger Equation and Related Problems

摘要

A methodology for the construction of efficient hybrid multistep methods for the numerical solution of second order initial or boundary-value problems with periodical or oscillating solutions is presented in this paper. This new methodology is based on the vanishing phase-lag and its derivatives on its level of the hybrid method. We apply the new methodology on a four-step hybrid type methods of sixth algebraic order. We will present a comparative error and stability analysis for the obtained new method. We will apply the new developed method to the resonance problem of the Schrodinger equation in order to show its efficiency.