RT - Journal Article T1 - A New High Order Closed Newton-Cotes Trigonometrically-fitted Formulae for the Numerical Solution of the Schrodinger Equation JF - IJMSI YR - 2018 JO - IJMSI VO - 13 IS - 1 UR - http://ijmsi.ir/article-1-785-en.html SP - 111 EP - 129 K1 - Phase-lag K1 - Schrodinger equation K1 - Numerical solution K1 - Newton-Cotes formulae K1 - Derivative AB - In this paper, we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted methods, symplectic integrators and efficient integration of the Schr¨odinger equation. The study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry (see the relevant literature and the references here). In this paper we study the closed Newton-Cotes formulae and we write them as symplectic multilayer structures. Based on the closed Newton-Cotes formulae, we also develop trigonometrically-fitted symplectic methods. An error analysis for the onedimensional Schrodinger equation of the new developed methods and a comparison with previous developed methods is also given. We apply the new symplectic schemes to the well-known radial Schr¨odinger equation in order to investigate the efficiency of the proposed method to these type of problems. LA eng UL http://ijmsi.ir/article-1-785-en.html M3 ER -