Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 867948, 12 pages
Research Article

An Optimized Runge-Kutta Method for the Numerical Solution of the Radial Schrödinger Equation

School of Mathematics and Statistics, Zaozhuang University, Zaozhuang 277160, China

Received 20 July 2012; Accepted 30 August 2012

Academic Editor: Gradimir Milovanovic

Copyright © 2012 Qinghe Ming 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.


An optimized explicit modified Runge-Kutta (RK) method for the numerical integration of the radial Schrödinger equation is presented in this paper. This method has frequency-depending coefficients with vanishing dispersion, dissipation, and the first derivative of dispersion. Stability and phase analysis of the new method are examined. The numerical results in the integration of the radial Schrödinger equation with the Woods-Saxon potential are reported to show the high efficiency of the new method.