A new methodology for the construction of optimized Runge-Kutta- Nystr?m methods

摘要

In this paper, a new Runge-Kutta-Nystr?m method of fourth algebraic order is developed. The new method has zero phase-lag, zero amplification error and zero first integrals of the previous properties. Numerical results indicate that the new method is very efficient for solving numerically the Schr?dinger equation. We note that for the first time in the literature we use the requirement of vanishing the first integrals of phase-lag and amplification error in the construction of efficient methods for the numerical solution of the Schr?dinger equation.