Abstract and Applied Analysis
Volume 2013 (2013), Article ID 910624, 11 pages
http://dx.doi.org/10.1155/2013/910624
Research Article

The Use of Phase Lag and Amplification Error Derivatives for the Construction of a Modified Runge-Kutta-Nyström Method

D. F. Papadopoulos1 and T. E. Simos2,3

1Department of Business Administration, Faculty of Management and Economy, Technological Educational Institute of Patras, 26 334 Patras, Greece
2Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
3Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, 22 100 Tripolis, Greece

Received 14 November 2012; Revised 16 March 2013; Accepted 3 April 2013

Academic Editor: Juan Carlos Cortés López

Copyright © 2013 D. F. Papadopoulos and T. 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.

Abstract

A new modified Runge-Kutta-Nyström method of fourth algebraic order is developed. The new modified RKN method is based on the fitting of the coefficients, due to the nullification not only of the phase lag and of the amplification error, but also of their derivatives. Numerical results indicate that the new modified method is much more efficient than other methods derived for solving numerically the Schrödinger equation.