TY - JOUR
JF - IJMSI
JO - IJMSI
VL - 13
IS - 1
PY - 2018
Y1 - 2018/5/01
TI - A New High Order Closed Newton-Cotes Trigonometrically-fitted Formulae for the Numerical Solution of the Schrodinger Equation
TT -
N2 - 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.
SP - 111
EP - 129
AU - Shokri, A.
AU - Saadat, H.
AU - Khodadadi, A. R.
AD - Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran
KW - Phase-lag
KW - Schrodinger equation
KW - Numerical solution
KW - Newton-Cotes formulae
KW - Derivative
UR - http://ijmsi.ir/article-1-785-en.html
ER -