High order computationally economical six-step method with vanished phase-lag and its derivatives for the numerical solution of the Schrodinger equation

摘要

A computationally economical symmetric six-step algorithm with high algebraic and phase-lag order is obtained in this paper, for the first time in the literature. Some characteristics of the new algorithm are: (1) algebraic order ten tenth, (2) eliminated phase-lag and its first, second, third, fourth and fifth derivatives, (3) the first layer is an approximation on the point and no at the usual point . A detailed analysis is also presented. In order to evaluate the efficiency of the new algorithm, we compare it with other well known and recently developed algorithms on three stages of evaluation: (1) evaluation based on local truncation error. (2) Evaluation based on stability analysis. (3) Evaluation based on accuracy and computational efficiency of the numerical approximation of the Schrodinger equation. Based on the above analysis, we arrive to the conclusion that the new developed method is more effective than other well known or recently produced methods of the literature.