Abstract.

In this paper, we present a new eight-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 Schr ̈odinger equation. Numerical stability and phase properties of the new methods are analyzed and the periodicity region of the method has been plotted. Finally we compare the new method to the corresponding classical ones and other known methods from the literature to demonstrate the high efficiency of our new method.

Keywords:

Schr ̈odinger equation, phase-lag, ordinary differential equations, P-stability, singu- larly P-stability.