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Advances in Mathematical Physics
Volume 2016, Article ID 8181927, 20 pages
Research Article

An Efficient Numerical Method for the Solution of the Schrödinger Equation

1School of Information Engineering, Chang’an University, Xi’an 710064, China
2Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
3Laboratory of Computational Sciences, Department of Informatics and Telecommunications, Faculty of Economy, Management and Informatics, University of Peloponnese, 221 00 Tripolis, Greece

Received 27 May 2016; Accepted 5 July 2016

Academic Editor: Maria L. Gandarias

Copyright © 2016 Licheng Zhang and Theodore E. Simos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The development of a new five-stage symmetric two-step fourteenth-algebraic order method with vanished phase-lag and its first, second, and third derivatives is presented in this paper for the first time in the literature. More specifically we will study the development of the new method, the determination of the local truncation error (LTE) of the new method, the local truncation error analysis which will be based on test equation which is the radial time independent Schrödinger equation, the stability and the interval of periodicity analysis of the new developed method which will be based on a scalar test equation with frequency different than the frequency of the scalar test equation used for the phase-lag analysis, and the efficiency of the new obtained method based on its application to the coupled Schrödinger equations.