A new four stages symmetric two-step method with vanished phase-lag and its first derivative for the numerical integration of the Schrodinger equation

摘要

In this paper a four stages symmetric two-step method with vanished phase-lag and its first derivative with high algebraic order is developed for the first time in the literature. More pricesly in this paper the following are presented: (1) the phase-lag analysis for the construction of the new high algebraic order method, (2) the construction of the new method, (3) the error analysis based on the radial Schrodinger equation, (4) the interval of periodicity analysis and the stability analysis, (5) a new error estimation procedure based on the phase-lag (6) the numerical tests for the study of the efficiency of the new obtained method which are based on the numerical solution of the Schrodinger equation.