A new implicit high-order six-step singularly P-stable method for the numerical solution of Schrödinger equation

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.