Hossein Saadat - Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran

Classical open and closed Newton-Cotes differential methods possessing the characteristics of multilayersymplectic structures have been constructed in the past. In this paper we present a new optimized symmetric six-stepof trigonometrically fitted predictor-corrector method, in which we apply the open and closed Newton-Cotesmethods for explicit and implicit methods respectively. We apply the symplectic schemes in order to solve theresonance problem of the radial Schrödinger equation. We measure the efficiency of the methods and conclude thatthe new method is the most efficient of all the compared methods

trigonometrically fitted, Schrödinger equation, Numerical solution, Newton-Cotes formulae, symplecticschemes