Dissipative high phase-lag order Numerov-type methods for the numerical solution of the Schrodinger equation

A generator of families of explicit hybrid methods with minimal phase lag i s developed in this paper. The methods of the generator have algebraic orde r six. The main characteristic of the new methods is that they are dissipat ive, i.e., they are not symmetric and they have not an interval of periodic ity. The generator is of dissipation order eight. Numerical results indicat e that these new methods are more efficient than older ones, i.e., the prop erty of the phase lag is more crucial than the nonempty interval of periodi city for the construction of the numerical methods for the numerical soluti on of the Schrodinger-type equations.