A new implicit symmetric method of sixth algebraic order with vanished phase-lag and its first derivative for solving Schr?dinger's equation

摘要

In this article, we have developed an implicit symmetric four-step method of sixth algebraic order with vanished phase-lag and its first derivative.The error and stability analysis of this method are investigated, and its efficiency is tested by solving efficiently the one-dimensional time-independent Schr?dinger’s equation.The method performance is compared with other methods in the literature.It is found that for this problem the new method performs better than the compared methods.