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

Abstract EN

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.