An explicit four-step method with vanished phase-lag and its first and second derivatives

摘要

In this paper we will develop an explicit fourth algebraic order four-step method with phase-lag and its first and second derivatives vanished. The comparative error and the stability analysis of the above mentioned paper is also presented. The new obtained method is applied on the resonance problem of the Schr?dinger equationIn order in order to examine its efficiency. The theoretical and the computational results shown that the new obtained method is more efficient than other well known methods for the numerical solution of the Schr?dinger equation and related initial-value or boundary-value problems with periodic and/or oscillating solutions.