AN EXPLICIT TRIGONOMETRICALLY FITTED TEN-STEP METHOD WITH PHASE-LAG OF ORDER INFINITY FOR THE NUMERICAL SOLUTION OF THE RADIAL SCHRODINGER EQUATION

In this paper, we present a newly optimized symmetric explicit ten-step (predictor method) method with phase-lag of order infinity (phase-fitted). The method is based on the symmetric multistep method of Quinlan Tremaine, with ten steps and tenth algebraic order, and is constructed to solve numerically the radial time-independent Schrodinger equation during the resonance problem with the use of the Woods-Saxon potential. It can also be used to integrate related IVPs with oscillating solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. 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