In this paper, we present a new implicit six-step singularly P-stable method with
vanished phase-lag and its derivatives up to fifth order for the numerical integration
of the one-dimensional radial time independent Schrödinger equation. The periodicity
region of the method is plotted and the numerical stability and phase properties
of the new methods are analyzed. The advantage of the new method in comparison
with similar methods—in terms of efficiency, accuracy and stability—have been
shown by implementing them in the radial time-independent Schrödinger equation
during the resonance problems with the use of the Woods–Saxon potential