On the Explicit Four-Step Methods with Vanished Phase-Lag and its First Derivative

Authors

T. E. Simos, Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia\\ Laboratory of Computational Sciences, Department of Informatics and Telecommunications, Faculty of Economy, Management and Informatics, University of Peloponnese, GR-221 00 Tripolis, GreeceFollow

Author Country (or Countries)

Greece

Abstract

In the present paper, we will investigate a family of explicit four-step methods first introduced by Anastassi and Simos [1] for the case of vanishing of phase-lag and its first derivative. These methods are efficient for the numerical solution of the Schr¨odinger equation and related initial-value or boundary-value problems with periodic and/or oscillating solutions. As we mentioned before the main scope of this paper is the study of the elimination of the phase-lag and its first derivative of the family of the methods to be investigated. A comparative error and stability analysis will be presented for the studied family of four-step explicit methods. The new obtained methods will finally be tested on the resonance problem of the Schr¨odinger equation in order to examine their efficiency.

Suggested Reviewers

N/A

Digital Object Identifier (DOI)

http://dx.doi.org/10.12785/amis/080201

Recommended Citation

E. Simos, T. (2014) "On the Explicit Four-Step Methods with Vanished Phase-Lag and its First Derivative," Applied Mathematics & Information Sciences: Vol. 08: Iss. 2, Article 1.
DOI: http://dx.doi.org/10.12785/amis/080201
Available at: https://digitalcommons.aaru.edu.jo/amis/vol08/iss2/1