A hybrid type four-step method with vanished phase-lag and its first, second and third derivatives for each level for the numerical integration of the Schrodinger equation

In this paper, we study the effects of the vanishing of the phase-lag and its first, second and third derivatives on the effectiveness of a four-step hybrid type method of sixth algebraic order. As a result of the above described study, a Hybrid type of three level four-step method of sixth algebraic order is obtained. We investigate the new produced method theoretically and computationally. The theoretical investigation of the new hybrid method consists of: The computation of the Local Truncation Error. The Comparison of the Local Truncation Error analysis with other known methods of the same form. The Stability Analysis. The computational investigation consists of the application of the new obtained hybrid method to the numerical solution of the resonance problem of the radial time independent Schrdinger equation.