Abstract and Applied Analysis
Volume 2012 (2012), Article ID 641236, 15 pages
http://dx.doi.org/10.1155/2012/641236
Research Article

A New Optimized Runge-Kutta Pair for the Numerical Solution of the Radial Schrödinger Equation

Yonglei Fang,1 Qinghong Li,2 Qinghe Ming,1 and Kaimin Wang1

1School of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277160, China
2Department of Mathematics, Chuzhou University, Chuzhou 239000, China

Received 9 May 2012; Revised 23 September 2012; Accepted 9 October 2012

Academic Editor: Malisa R. Zizovic

Copyright © 2012 Yonglei Fang et al. 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 embedded pair of explicit modified Runge-Kutta (RK) methods for the numerical integration of the radial Schrödinger equation is presented. The two RK methods in the pair have algebraic orders five and four, respectively. The two methods of the embedded pair are derived by nullifying the phase lag, the first derivative of the phase lag of the fifth-order method, and the phase lag of the fourth-order method. Nu merical experiments show the efficiency and robustness of our new methods compared with some well-known integrators in the literature.