Numerical solution of Schrodinger equation using compact finite differences method and the cubic spline functions

Abstract

In this paper, a high-order method for solving the Schrodinger equation is introduced. We apply a compact finite difference approximation for discretizing spatial derivatives and we use the C1-cubic spline collocation method for the time integration of the resulting linear system of ordinary differential equations. The proposed method has fourth-order accuracy in both space and time variables. We can obtain both pointwise approximations at the all mesh points and, a cubic spline solution in each space step by the method. Numerical results show that the method is an efficient technique for solving the one-dimensional Schrodinger equation.Â