A New Four-Stages Twelfth Algebraic Order Two-Step Method with Vanished Phase-Lag and Its First, Second, Third and Fourth Derivatives for the Numerical Solution of the Schrodinger Equation

摘要

In this paper we obtain, for the first time in the literature, a new twelfth algebraic order four stages symmetric two step method. The method is produced, i.e. its coefficients are determined, by requiring the vanishing of the phase lag and its first, second, third and fourth derivatives and by requesting additionally the highest possible algebraic order. The result of the elimination of the phase lag and its derivatives on the effectiveness of the new obtained method is also studied. The following are investigated: