The new class of explicit four-step methods with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation

In this paper, we present a family new optimized symmetric explicit multistep method with vanished phase-lag and its first derivative. The method is based on the symmetric multistep method of Quinlan Tremaine, and is constructed to solve numerically the radial time-independent Schrödinger equation during the resonance problem with the use of the Woods-Saxon potential. We measure the efficiency of the methods and conclude that the new method with infinite order of phase-lag is the most efficient of all the compared methods and for all the problems solved.