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

A family of new hybrid explicit four-step tenth algebraic order methods wit h phase lag of order 18(2)26 is developed for efficient computations of the Schrodinger equation. Based on these new methods, a new embedded variable- step method is obtained. Numerical results produced for the numerical solut ion of the coupled equations arising from the Schrodinger equation show tha t the new method is better than other variable-step methods. (C) 1999 John Wiley & Sons, Inc.