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.
Articles you may be interested inA new approach to construct Runge-Kutta type methods and geometric numerical integrators AIP Conf.Abstract. In this paper, we present a novel Runge-Kutta method especially designed for the numerical integration of stiff oscillatory problems with two-frequency. The new method can exactly integrate the harmonic or unperturbed oscillators with different frequencies. Numerical stability and phase properties of the new method are analyzed. Numerical experiments are carried out to show the efficiency and robustness of our new method in comparison with the well known methods.
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