A modified phase-fitted and amplification-fitted Runge-Kutta-Nystr?m method for the numerical solution of the radial Schr?dinger equation

摘要

A new Runge-Kutta-Nystr?m method, with phase-lag and amplification error of order infinity, for the numerical solution of the Schr?dinger equation is developed in this paper. The new method is based on the Runge-Kutta-Nystr?m method with fourth algebraic order, developed by Dormand, El-Mikkawy and Prince. Numerical illustrations indicate that the new method is much more efficient than other methods derived for the same purpose.