A new embedded 5(3) pair of modified Runge-Kutta-Nystr?m methods for the numerical solution of the Schr?dinger equation

摘要

A new embedded 5(3) pair of modified Runge-Kutta-Nystr?m methods for the numerical solution of the Schr?dinger equation is developed in this paper. The asymptotic expressions of the principal local truncation errors for large energies are obtained. We apply the new fifth-order method to the resonance problem, and apply the new embedded 5(3) pair to elastic scattering phase-shift problem. The numerical results showgood numerical performance of the newembedded pair and the fifth-order method.