A symmetric eight-step predictor-corrector method for the numerical solution of the radial Schrödinger equation and related IVPs with oscillating solutions

► Development of a highly efficient predictor-corrector method with zero phase-lag. ► New implementation technique of predictor-corrector methods with decreased CPU cost. ► Error analysis and periodicity analysis indicate the superiority of the new method. ► Numerical results comparing the new method to many others for 7 IVPs.