High algebraic order explicit methods with reduced phase-lag for an efficient solution of the Schr�dinger equation

Abstract

A family of new hybrid explicit four-step tenth algebraic order methods with phase lag of order 18(2)26 is developed for efficient computations of the Schrödinger equation. Based on these new methods, a new embedded variable-step method is obtained. Numerical results produced for the numerical solution of the coupled equations arising from the Schrödinger equation show that the new method is better than other variable-step methods. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 479–496, 1999